Quantum criticality: competing ground states in low dimensions

Bullet pressure-cell design for neutron scattering experiments with horizontal magnetic fields and dilution temperatures

The simultaneous application of high magnetic fields and high pressures for controlling magnetic ground states is important for testing our understanding of many-body quantum theory. However, the implementation for neutron scattering experiments presents a technical challenge. To overcome this challenge, we present an optimized pressure-cell design with a novel bullet shape, which is compatible with horizontal-field magnets, in particular the high-field magnet operating at the Helmholtz-Zentrum Berlin. The cell enabled neutron diffraction and spectroscopy measurements with the combination of three extreme conditions: high pressures, high magnetic fields, and dilution temperatures, simultaneously reaching 0.7 GPa, 25.9 T, and 200 mK, respectively. Our results demonstrate the utility of informed material choices and the efficiency of finite-element analysis for future pressure-cell designs to be used in combination with magnetic fields and dilution temperatures for neutron scattering purposes.

Pressure-tuned quantum criticality in the large-D antiferromagnet DTN

Strongly correlated spin systems can be driven to quantum critical points via various routes. In particular, gapped quantum antiferromagnets can undergo phase transitions into a magnetically ordered state with applied pressure or magnetic field, acting as tuning parameters. These transitions are characterized by z = 1 or z = 2 dynamical critical exponents, determined by the linear and quadratic low-energy dispersion of spin excitations, respectively. Employing high-frequency susceptibility and ultrasound techniques, we demonstrate that the tetragonal easy-plane quantum antiferromagnet NiCl2 ⋅ 4SC(NH2)2 (aka DTN) undergoes a spin-gap closure transition at about 4.2 kbar, resulting in a pressure-induced magnetic ordering. The studies are complemented by high-pressure-electron spin-resonance measurements confirming the proposed scenario. Powder neutron diffraction measurements revealed that no lattice distortion occurs at this pressure and the high spin symmetry is preserved, establishing DTN as a perfect platform to investigate z = 1 quantum critical phenomena. The experimental observations are supported by DMRG calculations, allowing us to quantitatively describe the pressure-driven evolution of critical fields and spin-Hamiltonian parameters in DTN.

Quantum criticality in chains of planar rotors with dipolar interactions

In this work, we perform a density matrix renormalization group study of chains of planar rotors interacting via dipolar interactions. By exploring the ground state from weakly to strongly interacting rotors, we find the occurrence of a quantum phase transition between a disordered and a dipole-ordered quantum state. We show that the nature of the ordered state changes from ferroelectric to antiferroelectric when the relative orientation of the rotor planes varies and that this change requires no modification of the overall symmetry. The observed quantum phase transitions are characterized by critical exponents and central charges, which reveal different universality classes ranging from that of the (1 + 1)D Ising model to the 2D classical XY model.

Effects of third-neighbor interactions on the frustrated quantum Ising model

We investigate thermal and quantum phase transitions of the J_{1}-J_{2}-J_{3} transverse Ising model on the square lattice. The model is studied within a cluster mean-field decoupling, which allows us to describe phase diagrams and the free-energy landscape in the neighborhood of phase transitions. Our findings indicate that the third-neighbor coupling (J_{3}) can affect the nature of phase transitions of the model. In particular, ferromagnetic third-neighbor couplings favor the onset of continuous order-disorder phase transitions, eliminating the tricritical point of the superantiferromagnetic-paramagnetic (SAFM-PM) phase boundary. On the other hand, the enhancement of frustration introduced by weak antiferromagnetic J_{3} gives rise to the staggered dimer phase favoring the onset of discontinuous classical phase transitions. Moreover, we find that quantum annealed criticality (QAC), which takes place when the classical discontinuous phase transition becomes critical by the enhancement of quantum fluctuations introduced by the transverse magnetic field, is eliminated from the SAFM-PM phase boundary by a relatively weak ferromagnetic J_{3}. Nevertheless, this change in the nature of phase transitions can still be observed in the presence of antiferromagnetic third-neighbor couplings being also found in the staggered-dimer phase boundary. Therefore, our findings support that QAC persists under the presence of frustrated antiferromagnetic third-neighbor couplings and is suppressed when these couplings are ferromagnetic, suggesting that frustration plays a central role in the onset of QAC.

Two-dimensional heavy fermion in a monoatomic-layer Kondo lattice YbCu2

The Kondo effect between localized f-electrons and conductive carriers leads to exotic physical phenomena. Among them, heavy-fermion (HF) systems, in which massive effective carriers appear due to the Kondo effect, have fascinated many researchers. Dimensionality is also an important characteristic of the HF system, especially because it is strongly related to quantum criticality. However, the realization of the perfect two-dimensional (2D) HF materials is still a challenging topic. Here, we report the surface electronic structure of the monoatomic-layer Kondo lattice YbCu2 on a Cu(111) surface observed by synchrotron-based angle-resolved photoemission spectroscopy. The 2D conducting band and the Yb 4f state, located very close to the Fermi level, are observed. These bands are hybridized at low-temperature, forming the 2D HF state, with an evaluated coherence temperature of about 30 K. The effective mass of the 2D state is enhanced by a factor of 100 by the development of the HF state. Furthermore, clear evidence of the hybridization gap formation in the temperature dependence of the Kondo-resonance peak has been observed below the coherence temperature. Our study provides a new candidate as an ideal 2D HF material for understanding the Kondo effect at low dimensions.

Quantum criticality at cryogenic melting of polar bubble lattices

Quantum fluctuations (QFs) caused by zero-point phonon vibrations (ZPPVs) are known to prevent the occurrence of polar phases in bulk incipient ferroelectrics down to 0 K. On the other hand, little is known about the effects of QFs on the recently discovered topological patterns in ferroelectric nanostructures. Here, by using an atomistic effective Hamiltonian within classical Monte Carlo (CMC) and path integral quantum Monte Carlo (PI-QMC), we unveil how QFs affect the topology of several dipolar phases in ultrathin Pb(Zr0.4Ti0.6)O3 (PZT) films. In particular, our PI-QMC simulations show that the ZPPVs do not suppress polar patterns but rather stabilize the labyrinth, bimeron and bubble phases within a wider range of bias field magnitudes. Moreover, we reveal that quantum fluctuations induce a quantum critical point (QCP) separating a hexagonal bubble lattice from a liquid-like state characterized by spontaneous motion, creation and annihilation of polar bubbles at cryogenic temperatures. Finally, we show that the discovered quantum melting is associated with anomalous physical response, as, e.g., demonstrated by a negative longitudinal piezoelectric coefficient.

Nano-Patterned Magnetic Edges in CrGeTe3 for Quasi 1-D Spintronic Devices

The synthesis of two-dimensional van der Waals magnets has paved the way for both technological applications and fundamental research on magnetism confined to ultra-small length scales. Edge magnetic moments in ferromagnets are expected to be less magnetized than in the sample interior because of the reduced amount of neighboring ferromagnetic spins at the sample edge. We recently demonstrated that CrGeTe₃ (CGT) flakes thinner than 10 nm are hard ferromagnets; i.e., they exhibit an open hysteresis loop. In contrast, thicker flakes exhibit zero net remnant field in the interior, with hard ferromagnetism present only at the cleaved edges. This experimental observation suggests that a nontrivial interaction exists between the sample edge and the interior. Here, we demonstrate that artificial edges fabricated by focus ion beam etching also display hard ferromagnetism. This enables us to write magnetic nanowires in CGT directly and use this method to characterize the magnetic interaction between the interior and edge. The results indicate that the interior saturation and depolarization fields depend on the lateral dimensions of the sample. Most notably, the interior region between the edges of a sample narrower than 300 nm becomes a hard ferromagnet, suggesting an enhancement of the magnetic exchange induced by the proximity of the edges. Last, we find that the CGT regions amorphized by the gallium beam are nonmagnetic, which introduces a novel method to tune the local magnetic properties of CGT films, potentially enabling integration into spintronic devices.

Partitioning the Two-Leg Spin Ladder in Ba2Cu1 - x Zn x TeO6: From Magnetic Order through Spin-Freezing to Paramagnetism

Ba₂CuTeO₆ has attracted significant attention as it contains a two-leg spin ladder of Cu²⁺ cations that lies in close proximity to a quantum critical point. Recently, Ba₂CuTeO₆ has been shown to accommodate chemical substitutions, which can significantly tune its magnetic behavior. Here, we investigate the effects of substitution for non-magnetic Zn²⁺ impurities at the Cu²⁺ site, partitioning the spin ladders. Results from bulk thermodynamic and local muon magnetic characterization on the Ba₂Cu_1 - x Zn _x TeO₆ solid solution (0 ≤ x ≤ 0.6) indicate that Zn²⁺ partitions the Cu²⁺ spin ladders into clusters and can be considered using the percolation theory. As the average cluster size decreases with increasing Zn²⁺ substitution, there is an evolving transition from long-range order to spin-freezing as the critical cluster size is reached between x = 0.1 to x = 0.2, beyond which the behavior became paramagnetic. This demonstrates well-controlled tuning of the magnetic disorder, which is highly topical across a range of low-dimensional Cu²⁺-based materials. However, in many of these cases, the chemical disorder is also relatively strong in contrast to Ba₂CuTeO₆ and its derivatives. Therefore, Ba₂Cu_1 - x Zn _x TeO₆ provides an ideal model system for isolating the effect of defects and segmentation in low-dimensional quantum magnets.

Quantum Phase Transition in the One-Dimensional Water Chain

The concept of quantum phase transitions (QPTs) plays a central role in the description of condensed matter systems. In this Letter, we perform high-quality wave-function-based simulations to demonstrate the existence of a quantum phase transition in a crucially relevant molecular system, namely, water, forming linear chains of rotating molecules. We determine various critical exponents and reveal the water chain QPT to belong to the (1+1)-dimensional Ising universality class. Furthermore, the effect of breaking symmetries is examined, and it is shown that, by breaking the inversion symmetry, the ground state degeneracy of the ordered quantum phase is lifted to yield two many-body states with opposite polarization. The possibility of forming ferroelectric phases together with a thermal stability of the quantum critical regime up to ∼10  K makes the linear water chain a promising candidate as a platform for quantum devices.

Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

The phenomena of quantum criticality underlie many novel collective phenomena found in condensed matter systems. They present a challenge for classical and quantum simulation, in part because of diverging correlation lengths and consequently strong finite-size effects. Tensor network techniques that work directly in the thermodynamic limit can negotiate some of these difficulties. Here, we optimise a translationally invariant, sequential quantum circuit on a superconducting quantum device to simulate the groundstate of the quantum Ising model through its quantum critical point. We further demonstrate how the dynamical quantum critical point found in quenches of this model across its quantum critical point can be simulated. Our approach avoids finite-size scaling effects by using sequential quantum circuits inspired by infinite matrix product states. We provide efficient circuits and a variety of error mitigation strategies to implement, optimise and time-evolve these states.

Correlation anisotropy driven Kosterlitz-Thouless-type quantum phase transition in a Kondo simulator

The precise manipulation of the quantum states of individual atoms/molecules adsorbed on metal surfaces is one of the most exciting frontiers in nanophysics, enabling us to realize novel single molecular logic devices and quantum information processing. Herein, by modeling an iron phthalocyanine molecule adsorbed on the Au(111) surface with a two-impurity Anderson model, we demonstrate that the quantum states of such a system could be adjusted by the uniaxial magnetic anisotropy D_z. For negative D_z, the ground state is dominated by a parallel configuration of the z component of local spins, whereas it turns to be an antiparallel one when D_z becomes positive. Interestingly, we found that these two phases are separated by a Kosterlitz-Thouless-type quantum phase transition, which is confirmed by the critical behaviors of the transmission coefficient and the local magnetic moment. Both phases are associated with spin correlation anisotropy, thus move against the Kondo effect. When the external magnetic field is applied, it first plays a role in compensating for the effect of D_z, and then it contributes significantly to the Zeeman effect for positive D_z, accompanied by the reappearance and the splitting of the Kondo peak, respectively. For fixed negative D_z, only the Zeeman behavior is revealed. Our results provide deep insights into the manipulation of the quantum phase within a single molecular junction.

Site-Selective d10/d0 Substitution in an S = 1/2 Spin Ladder Ba2CuTe1-xWxO6 (0 ≤ x ≤ 0.3)

Isovalent nonmagnetic d10 and d0 B″ cations have proven to be a powerful tool for tuning the magnetic interactions between magnetic B' cations in A2B'B″O6 double perovskites. Tuning is facilitated by the changes in orbital hybridization that favor different superexchange pathways. This can produce alternative magnetic structures when B″ is d10 or d0. Furthermore, the competition generated by introducing mixtures of d10 and d0 cations can drive the material into the realms of exotic quantum magnetism. Here, Te6+ d10 was substituted by W6+ d0 in the hexagonal perovskite Ba2CuTeO6, which possesses a spin ladder geometry of Cu2+ cations, creating a Ba2CuTe1-xWxO6 solid solution (x = 0-0.3). We find W6+ is almost exclusively substituted for Te6+ on the corner-sharing site within the spin ladder, in preference to the face-sharing site between ladders. The site-selective doping directly tunes the intraladder, Jrung and Jleg, interactions. Modeling the magnetic susceptibility data shows the d0 orbitals modify the relative intraladder interaction strength (Jrung/Jleg) so the system changes from a spin ladder to isolated spin chains as W6+ increases. This further demonstrates the utility of d10 and d0 dopants as a tool for tuning magnetic interactions in a wide range of perovskites and perovskite-derived structures.

Thermally driven state in a spin-1 model with competing interactions

We study a recently proposed spin-1 model with competing antiferromagnetic first-neighbor interaction and a third-neighbor coupling mediated by nonmagnetic states, which reproduces topological features of the phase diagrams of high-T_{c} superconductors [S. A. Cannas and D. A. Stariolo, Phys. Rev. E 99, 042137 (2019)2470-004510.1103/PhysRevE.99.042137]. We employ a cluster mean-field approach to investigate effects of crystal field anisotropy on the phase transitions hosted by this model. At low temperatures, the temperature-crystal field phase diagram exhibits superantiferromagnetic (SAF), antiferromagnetic (AF), and paramagnetic (PM) phases. In addition, we found a thermally driven state between SAF and PM phases. This thermally driven state and the SAF phase appears in the phase diagram as a domelike structure. Our calculations indicate that only second-order phase transitions occur in the PM-AF phase boundary, as suggested by previous Monte Carlo simulations.

Strongly correlated Fermions strongly coupled to light

Strong quantum correlations in matter are responsible for some of the most extraordinary properties of materials, from magnetism to high-temperature superconductivity, but their integration in quantum devices requires a strong, coherent coupling with photons, which still represents a formidable technical challenge in solid state systems. In cavity quantum electrodynamics, quantum gases such as Bose-Einstein condensates or lattice gases have been strongly coupled with light. However, neither Fermionic quantum matter, comparable to electrons in solids, nor atomic systems with controlled interactions, have thus far been strongly coupled with photons. Here we report on the strong coupling of a quantum-degenerate unitary Fermi gas with light in a high finesse cavity. We map out the spectrum of the coupled system and observe well resolved dressed states, resulting from the strong coupling of cavity photons with each spin component of the gas. We investigate spin-balanced and spin-polarized gases and find quantitative agreement with ab initio calculation describing light-matter interaction. Our system offers complete and simultaneous control of atom-atom and atom-photon interactions in the quantum degenerate regime, opening a wide range of perspectives for quantum simulation.

Global Phase Diagram of a Spin-Orbital Kondo Impurity Model and the Suppression of Fermi-Liquid Scale

Many correlated metallic materials are described by Landau Fermi-liquid theory at low energies, but for Hund metals the Fermi-liquid coherence scale T_{FL} is found to be surprisingly small. In this Letter, we study the simplest impurity model relevant for Hund metals, the three-channel spin-orbital Kondo model, using the numerical renormalization group (NRG) method and compute its global phase diagram. In this framework, T_{FL} becomes arbitrarily small close to two new quantum critical points that we identify by tuning the spin or spin-orbital Kondo couplings into the ferromagnetic regimes. We find quantum phase transitions to a singular Fermi-liquid or a novel non-Fermi-liquid phase. The new non-Fermi-liquid phase shows frustrated behavior involving alternating overscreenings in spin and orbital sectors, with universal power laws in the spin (ω^{-1/5}), orbital (ω^{1/5}) and spin-orbital (ω^{1}) dynamical susceptibilities. These power laws, and the NRG eigenlevel spectra, can be fully understood using conformal field theory arguments, which also clarify the nature of the non-Fermi-liquid phase.

Logarithmic Upturn in Low-Temperature Electronic Transport as a Signature of d-Wave Order in Cuprate Superconductors

In cuprate superconductors, high magnetic fields have been used extensively to suppress superconductivity and expose the underlying normal state. Early measurements revealed insulatinglike behavior in underdoped material versus temperature T, in which resistivity increases on cooling with a puzzling log(1/T) form. We instead use microwave measurements of flux-flow resistivity in YBa_{2}Cu_{3}O_{6+y} and Tl_{2}Ba_{2}CuO_{6+δ} to study charge transport deep inside the superconducting phase, in the low-temperature and low-field regime. Here, the transition from metallic low-temperature resistivity (dρ/dT>0) to a log(1/T) upturn persists throughout the superconducting doping range, including a regime at high carrier dopings in which the field-revealed normal-state resistivity is Fermi-liquid-like. The log(1/T) form is thus likely a signature of d-wave superconducting order, and the field-revealed normal state's log(1/T) resistivity may indicate the free-flux-flow regime of a phase-disordered d-wave superconductor.

Quantum Magnetic Properties in Perovskite with Anderson Localized Artificial Spin-1/2

Quantum magnetic properties in a geometrically frustrated lattice of spin-1/2 magnet, such as quantum spin liquid or solid and the associated spin fractionalization, are considered key in developing a new phase of matter. The feasibility of observing the quantum magnetic properties, usually found in geometrically frustrated lattice of spin-1/2 magnet, in a perovskite material with controlled disorder is demonstrated. It is found that the controlled chemical disorder, due to the chemical substitution of Ru ions by Co-ions, in a simple perovskite CaRuO3 creates a random prototype configuration of artificial spin-1/2 that forms dimer pairs between the nearest and further away ions. The localization of the Co impurity in the Ru matrix is analyzed using the Anderson localization formulation. The dimers of artificial spin-1/2, due to the localization of Co impurities, exhibit singlet-to-triplet excitation at low temperature without any ordered spin correlation. The localized gapped excitation evolves into a gapless quasi-continuum as dimer pairs break and create freely fluctuating fractionalized spins at high temperature. Together, these properties hint at a new quantum magnetic state with strong resemblance to the resonance valence bond system.

Comparative approximations of criticality in a neural and quantum regime

Under a variety of conditions, stochastic and non-linear systems with many degrees of freedom tend to evolve towards complexity and criticality. Over the last decades, a steady proliferation of models re: far-from-equilibrium thermodynamics of metastable, many-valued systems arose, serving as attributes of a 'critical' attractor landscape. Building off recent data citing trademark aspects of criticality in the brain-including: power-laws, scale-free (1/f) behavior (scale invariance, or scale independence), critical slowing, and avalanches-it has been conjectured that operating at criticality entails functional advantages such as: optimized neural computation and information processing; boosted memory; large dynamical ranges; long-range communication; and an increased ability to react to highly diverse stimuli. In short, critical dynamics provide a necessary condition for neurobiologically significant elements of brain dynamics. Theoretical predictions have been verified in specific models such as Boolean networks, liquid state machines, and neural networks. These findings inspired the neural criticality hypothesis, proposing that the brain operates in a critical state because the associated optimal computational capabilities provide an evolutionarily advantage. This paper develops in three parts: after developing the critical landscape, we will then shift gears to rediscover another inroad to criticality via stochastic quantum field theory and dissipative dynamics. The existence of these two approaches deserves some consideration, given both neural and quantum criticality hypotheses propose specific mechanisms that leverage the same phenomena. This suggests that understanding the quantum approach could help to shed light on brain-based modeling. In the third part, we will turn to Whitehead's actual entities and modes of perception in order to demonstrate a concomitant logic underwriting both models. In the discussion, I briefly motivate a reading of criticality and its properties as responsive to the characterization of tenets from Eastern wisdom traditions.

Emergence of Quantum Critical Behavior in Metallic Quantum-Well States of Strongly Correlated Oxides

Controlling quantum critical phenomena in strongly correlated electron systems, which emerge in the neighborhood of a quantum phase transition, is a major challenge in modern condensed matter physics. Quantum critical phenomena are generated from the delicate balance between long-range order and its quantum fluctuation. So far, the nature of quantum phase transitions has been investigated by changing a limited number of external parameters such as pressure and magnetic field. We propose a new approach for investigating quantum criticality by changing the strength of quantum fluctuation that is controlled by the dimensional crossover in metallic quantum well (QW) structures of strongly correlated oxides. With reducing layer thickness to the critical thickness of metal-insulator transition, crossover from a Fermi liquid to a non-Fermi liquid has clearly been observed in the metallic QW of SrVO₃ by in situ angle-resolved photoemission spectroscopy. Non-Fermi liquid behavior with the critical exponent α = 1 is found to emerge in the two-dimensional limit of the metallic QW states, indicating that a quantum critical point exists in the neighborhood of the thickness-dependent Mott transition. These results suggest that artificial QW structures provide a unique platform for investigating novel quantum phenomena in strongly correlated oxides in a controllable fashion.

Itinerant magnetic metals

In this review, an overview of itinerant magnets without magnetic elements is presented, beginning with a comparison of the local and itinerant moment pictures, the two extremes of magnetism. Then, the theoretical developments leading up to the self-consistent renormalization theory of spin fluctuations will be discussed, followed by an introduction to quantum criticality and the experimental signatures associated with systems near a quantum critical point. Three itinerant magnets without magnetic elements, ZrZn₂, Sc_3.1In, and TiAu are the focus of this review, as their empty d shells set them apart in their purely itinerant character, while several enhanced Pauli paramagnets and intermediate moment magnets are also discussed to put the overall comparison into perspective.

Complementary Response of Static Spin-Stripe Order and Superconductivity to Nonmagnetic Impurities in Cuprates

We report muon-spin rotation and neutron-scattering experiments on nonmagnetic Zn impurity effects on the static spin-stripe order and superconductivity of the La214 cuprates. Remarkably, it was found that, for samples with hole doping x≈1/8, the spin-stripe ordering temperature T_{so} decreases linearly with Zn doping y and disappears at y≈4%, demonstrating a high sensitivity of static spin-stripe order to impurities within a CuO_{2} plane. Moreover, T_{so} is suppressed by Zn in the same manner as the superconducting transition temperature T_{c} for samples near optimal hole doping. This surprisingly similar sensitivity suggests that the spin-stripe order is dependent on intertwining with superconducting correlations.

Hidden phase in a two-dimensional Sn layer stabilized by modulation hole doping

Semiconductor surfaces and ultrathin interfaces exhibit an interesting variety of two-dimensional quantum matter phases, such as charge density waves, spin density waves and superconducting condensates. Yet, the electronic properties of these broken symmetry phases are extremely difficult to control due to the inherent difficulty of doping a strictly two-dimensional material without introducing chemical disorder. Here we successfully exploit a modulation doping scheme to uncover, in conjunction with a scanning tunnelling microscope tip-assist, a hidden equilibrium phase in a hole-doped bilayer of Sn on Si(111). This new phase is intrinsically phase separated into insulating domains with polar and nonpolar symmetries. Its formation involves a spontaneous symmetry breaking process that appears to be electronically driven, notwithstanding the lack of metallicity in this system. This modulation doping approach allows access to novel phases of matter, promising new avenues for exploring competing quantum matter phases on a silicon platform.

Broken symmetry phases may occur in 2D materials upon doping, yet introducing doping without inducing chemical disorder remains a challenge. Here, the authors use a modulation doping approach that unveils a hidden equilibrium phase involving spontaneous symmetry breaking in a hole-doped Sn bilayer.

Correlation-driven transport asymmetries through coupled spins in a tunnel junction

Spin-spin correlations can be the driving force that favours certain ground states and are key in numerous models that describe the behaviour of strongly correlated materials. While the sum of collective correlations usually lead to a macroscopically measurable change in properties, a direct quantification of correlations in atomic scale systems is difficult. Here we determine the correlations between a strongly hybridized spin impurity on the tip of a scanning tunnelling microscope and its electron bath by varying the coupling to a second spin impurity weakly hybridized to the sample surface. Electronic transport through these coupled spins reveals an asymmetry in the differential conductance reminiscent of spin-polarized transport in a magnetic field. We show that at zero field, this asymmetry can be controlled by the coupling strength and is related to either ferromagnetic or antiferromagnetic spin-spin correlations in the tip.

Candidate Elastic Quantum Critical Point in LaCu_{6-x}Au_{x}

The structural properties of LaCu_{6-x}Au_{x} are studied using neutron diffraction, x-ray diffraction, and heat capacity measurements. The continuous orthorhombic-monoclinic structural phase transition in LaCu_{6} is suppressed linearly with Au substitution until a complete suppression of the structural phase transition occurs at the critical composition x_{c}=0.3. Heat capacity measurements at low temperatures indicate residual structural instability at x_{c}. The instability is ferroelastic in nature, with density functional theory calculations showing negligible coupling to electronic states near the Fermi level. The data and calculations presented here are consistent with the zero temperature termination of a continuous structural phase transition suggesting that the LaCu_{6-x}Au_{x} series hosts an elastic quantum critical point.

Coexistence of charge and ferromagnetic order in fcc Fe

Phase coexistence phenomena have been intensively studied in strongly correlated materials where several ordered states simultaneously occur or compete. Material properties critically depend on external parameters and boundary conditions, where tiny changes result in qualitatively different ground states. However, up to date, phase coexistence phenomena have exclusively been reported for complex compounds composed of multiple elements. Here we show that charge- and magnetically ordered states coexist in double-layer Fe/Rh(001). Scanning tunnelling microscopy and spectroscopy measurements reveal periodic charge-order stripes below a temperature of 130 K. Close to liquid helium temperature, they are superimposed by ferromagnetic domains as observed by spin-polarized scanning tunnelling microscopy. Temperature-dependent measurements reveal a pronounced cross-talk between charge and spin order at the ferromagnetic ordering temperature about 70 K, which is successfully modelled within an effective Ginzburg-Landau ansatz including sixth-order terms. Our results show that subtle balance between structural modifications can lead to competing ordering phenomena.

Using Nonequilibrium Dynamics to Probe Competing Orders in a Mott-Peierls System

Competition between ordered phases, and their associated phase transitions, are significant in the study of strongly correlated systems. Here, we examine one aspect, the nonequilibrium dynamics of a photoexcited Mott-Peierls system, using an effective Peierls-Hubbard model and exact diagonalization. Near a transition where spin and charge become strongly intertwined, we observe antiphase dynamics and a coupling-strength-dependent suppression or enhancement in the static structure factors. The renormalized bosonic excitations coupled to a particular photoexcited electron can be extracted, which provides an approach for characterizing the underlying bosonic modes. The results from this analysis for different electronic momenta show an uneven softening due to a stronger coupling near k_{F}. This behavior reflects the strong link between the fermionic momenta, the coupling vertices, and ultimately, the bosonic susceptibilities when multiple phases compete for the ground state of the system.

Photon number statistics uncover the fluctuations in non-equilibrium lattice dynamics

Fluctuations of the atomic positions are at the core of a large class of unusual material properties ranging from quantum para-electricity to high temperature superconductivity. Their measurement in solids is the subject of an intense scientific debate focused on seeking a methodology capable of establishing a direct link between the variance of the atomic displacements and experimentally measurable observables. Here we address this issue by means of non-equilibrium optical experiments performed in shot-noise-limited regime. The variance of the time-dependent atomic positions and momenta is directly mapped into the quantum fluctuations of the photon number of the scattered probing light. A fully quantum description of the non-linear interaction between photonic and phononic fields is benchmarked by unveiling the squeezing of thermal phonons in α-quartz.

Quantum Critical Origin of the Superconducting Dome in SrTiO_{3}

We expand the well-known notion that quantum criticality can induce superconductivity by proposing a concrete mechanism for superconductivity due to quantum ferroelectric fluctuations. To this end, we investigate the origin of superconductivity in doped SrTiO_{3} using a combination of density functional and strong coupling theories within the framework of quantum criticality. Our density functional calculations of the ferroelectric soft mode frequency as a function of doping reveal a crossover related to quantum paraelectricity at a doping level coincident with the experimentally observed top of the superconducting dome. Thus, we suggest a model in which the soft mode fluctuations provide the pairing interaction for superconductivity carriers. Within our model, the low doping limit of the superconducting dome is explained by the emergence of the Fermi surface, and the high doping limit by departure from the quantum critical regime. We predict that the highest critical temperature will increase and shift to lower carrier doping with increasing ^{18}O isotope substitution, a scenario that is experimentally verifiable. Our model is applicable to other quantum paraelectrics, such as KTaO_{3}.

Spectroscopy of Interacting Quasiparticles in Trapped Ions

The static and dynamic properties of many-body quantum systems are often well described by collective excitations, known as quasiparticles. Engineered quantum systems offer the opportunity to study such emergent phenomena in a precisely controlled and otherwise inaccessible way. We present a spectroscopic technique to study artificial quantum matter and use it for characterizing quasiparticles in a many-body system of trapped atomic ions. Our approach is to excite combinations of the system's fundamental quasiparticle eigenmodes, given by delocalized spin waves. By observing the dynamical response to superpositions of such eigenmodes, we extract the system dispersion relation, magnetic order, and even detect signatures of quasiparticle interactions. Our technique is not limited to trapped ions, and it is suitable for verifying quantum simulators by tuning them into regimes where the collective excitations have a simple form.

Critical and near-critical phase behavior and interplay between the thermodynamic Casimir and van der Waals forces in a confined nonpolar fluid medium with competing surface and substrate potentials

We study, using general scaling arguments and mean-field type calculations, the behavior of the critical Casimir force and its interplay with the van der Waals force acting between two parallel slabs separated at a distance L from each other, confining some fluctuating fluid medium, say a nonpolar one-component fluid or a binary liquid mixture. The surfaces of the slabs are coated by thin layers exerting strong preference to the liquid phase of the fluid, or one of the components of the mixture, modeled by strong adsorbing local surface potentials ensuring the so-called (+,+) boundary conditions. The slabs, on the other hand, influence the fluid by long-range competing dispersion potentials, which represent irrelevant interactions in renormalization-group sense. Under such conditions, one usually expects attractive Casimir force governed by universal scaling function, pertinent to the extraordinary surface universality class of Ising type systems, to which the dispersion potentials provide only corrections to scaling. We demonstrate, however, that below a given threshold thickness of the system L(crit) for a suitable set of slabs-fluid and fluid-fluid coupling parameters the competition between the effects due to the coatings and the slabs can result in sign change of the Casimir force acting between the surfaces confining the fluid when one changes the temperature T, the chemical potential of the fluid μ, or L. The last implies that by choosing specific materials for the slabs, coatings, and the fluid for L≲L(crit) one can realize repulsive Casimir force with nonuniversal behavior which, upon increasing L, gradually turns into an attractive one described by a universal scaling function, depending only on the relevant scaling fields related to the temperature and the excess chemical potential, for L≫L(crit). We present arguments and relevant data for specific substances in support of the experimental feasibility of the predicted behavior of the force. It can be of interest, e.g., for designing nanodevices and for governing behavior of objects, say colloidal particles, at small distances. We formulate the corresponding criterion for determination of L(crit). The universality is regained for L≫L(crit). We also show that for systems with L≲L(crit), the capillary condensation phase diagram suffers modifications which one does not observe in systems with purely short-ranged interactions.

Measuring the dynamic structure factor of a quantum gas undergoing a structural phase transition

The dynamic structure factor is a central quantity describing the physics of quantum many-body systems, capturing structure and collective excitations of a material. In condensed matter, it can be measured via inelastic neutron scattering, which is an energy-resolving probe for the density fluctuations. In ultracold atoms, a similar approach could so far not be applied because of the diluteness of the system. Here we report on a direct, real-time and nondestructive measurement of the dynamic structure factor of a quantum gas exhibiting cavity-mediated long-range interactions. The technique relies on inelastic scattering of photons, stimulated by the enhanced vacuum field inside a high finesse optical cavity. We extract the density fluctuations, their energy and lifetime while the system undergoes a structural phase transition. We observe an occupation of the relevant quasi-particle mode on the level of a few excitations, and provide a theoretical description of this dissipative quantum many-body system.

Casimir force in the O(n→∞) model with free boundary conditions

We present results for the temperature behavior of the Casimir force for a system with a film geometry with thickness L subject to free boundary conditions and described by the n→∞ limit of the O(n) model. These results extend over all temperatures, including the critical regime near the bulk critical temperature Tc, where the critical fluctuations determine the behavior of the force, and temperatures well below it, where its behavior is dictated by the Goldstone mode contributions. The temperature behavior when the absolute temperature, T, is a finite distance below Tc, up to a logarithmic-in-L proximity of the bulk critical temperature, is obtained both analytically and numerically; the critical behavior follows from numerics. The results resemble-but do not duplicate-the experimental curve behavior for the force obtained for He4 films.

Evidence for dimer crystal melting in the frustrated spin-ladder system BiCu2PO6

In the spin ladder compound BiCu(2)PO(6), there exists a decisive dynamics of spin excitations that we classify and characterize using inelastic light scattering. We observe an interladder singlet bound mode at 24  cm(-1) and two intraladder bound states at 62 and 108  cm(-1) in the leg (bb) and the rung (cc) polarization as well as a broad triplon continuum extending from 36  cm(-1) to 700  cm(-1). Though isolated spin ladder physics can roughly account for the observed excitations at high energies, frustration and interladder interactions need to be considered to fully describe the spectral distribution and scattering selection rules at low and intermediate energies. In addition, we attribute the rich spectrum of singlet bound modes to a melting of a dimer crystal. Our study provides evidence for a Z(2) quantum phase transition from a dimer to a resonating valence bond state driven by singlet fluctuations.

Competition between the Pseudogap and superconducting states of Bi2Sr2Ca0.92Y0.08Cu2O8+δ single crystals revealed by ultrafast broadband optical reflectivity

Ultrafast broadband transient reflectivity experiments are performed to study the interplay between the nonequilibrium dynamics of the pseudogap and the superconducting phases in Bi(2)Sr(2}Ca(0.92)Y(0.08)Cu(2)O(8+δ). Once superconductivity is established, the relaxation of the pseudogap proceeds ~2 times faster than in the normal state, and the corresponding transient reflectivity variation changes sign after ~0.5 ps. The results can be described by a set of coupled differential equations for the pseudogap and for the superconducting order parameter. The sign and strength of the coupling term suggest a remarkably weak competition between the two phases, allowing their coexistence.

Quantum phase transition from triangular to stripe charge order in NbSe2

The competition between proximate electronic phases produces a complex phenomenology in strongly correlated systems. In particular, fluctuations associated with periodic charge or spin modulations, known as density waves, may lead to exotic superconductivity in several correlated materials. However, density waves have been difficult to isolate in the presence of chemical disorder, and the suspected causal link between competing density wave orders and high-temperature superconductivity is not understood. Here we used scanning tunneling microscopy to image a previously unknown unidirectional (stripe) charge-density wave (CDW) smoothly interfacing with the familiar tridirectional (triangular) CDW on the surface of the stoichiometric superconductor NbSe(2). Our low-temperature measurements rule out thermal fluctuations and point to local strain as the tuning parameter for this quantum phase transition. We use this quantum interface to resolve two longstanding debates about the anomalous spectroscopic gap and the role of Fermi surface nesting in the CDW phase of NbSe(2). Our results highlight the importance of local strain in governing phase transitions and competing phenomena, and suggest a promising direction of inquiry for resolving similarly longstanding debates in cuprate superconductors and other strongly correlated materials.

Dynamical matrix diagonalization for the calculation of dispersive excitations

The solid state exhibits a fascinating variety of phases, which can be stabilized by the variation of external parameters such as temperature, magnetic field and pressure. Until recently, numerical analysis of magnetic and/or orbital phases with collective excitations on a periodic lattice tended to be done on a case-by-case basis. Nowadays dynamical matrix diagonalization (DMD) has become an important and powerful standard method for the calculation of dispersive modes. The application of DMD to the interpretation of inelastic neutron scattering (INS) data on dispersive magnetic excitations is reviewed. A methodical survey of calculations employing spin-orbit and intermediate coupling schemes is illustrated by examples. These are taken from recent work on rare earth, actinide and transition metal compounds and demonstrate the application of the formalism developed.

Experimental quantum simulations of many-body physics with trapped ions

Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems.

Chemically mediated quantum criticality in NbFe2

Laves-phase Nb(1+c)Fe(2-c) is a rare itinerant intermetallic compound exhibiting magnetic quantum criticality at c(cr)∼1.5%Nb excess; its origin, and how alloying mediates it, remains an enigma. For NbFe(2), we show that an unconventional band critical point above the Fermi level E(F) explains most observations and that chemical alloying mediates access to this unconventional band critical point by an increase in E(F) with decreasing electrons (increasing %Nb), counter to rigid-band concepts. We calculate that E(F) enters the unconventional band critical point region for c(cr) > 1.5%Nb and by 1.74%Nb there is no Nb site-occupation preference between symmetry-distinct Fe sites, i.e., no electron-hopping disorder, making resistivity near constant as observed. At larger Nb (Fe) excess, the ferromagnetic Stoner criterion is satisfied.

Renormalization group study of random quantum magnets

We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse field Ising model, which is a prototype of random quantum magnets. With this algorithm we can renormalize an N-site cluster within a time NlogN, independently of the topology of the graph, and we went up to N ∼ 4 × 10(6). We have studied regular lattices with dimension D ≤ 4 as well as Erdős-Rényi random graphs, which are infinite dimensional objects. In all cases the quantum critical behaviour is found to be controlled by an infinite disorder fixed point, in which disorder plays a dominant role over quantum fluctuations. As a consequence the renormalization procedure as well as the obtained critical properties are asymptotically exact for large systems. We have also studied Griffiths singularities in the paramagnetic and ferromagnetic phases and generalized the numerical algorithm for other random quantum systems.

Magnetic susceptibility and heat capacity of a novel antiferromagnet: LiNi2P3O10 and the effect of doping

We report the synthesis, x-ray diffraction, magnetic susceptibility and specific heat measurements on polycrystalline samples of undoped LiNi(2)P(3)O(10) and samples with non-magnetic impurity (Zn(2+), S = 0) and magnetic impurity (Cu(2+), S = 1/2) at the Ni site. The magnetic susceptibility data show a broad maximum at around 10 K and a small anomaly at about 7 K in the undoped sample. There is a λ-like anomaly in the specific heat at 7 K, possibly due to the onset of antiferromagnetic ordering in the system. The magnetic entropy change at the ordering temperature is close to the value corresponding to Rln(2S + 1) expected for an S = 1 system. The temperature corresponding to the broad maximum and the ordering temperature both decrease on Zn and Cu substitutions and also in applied magnetic fields.

Signatures of quantum criticality in pure Cr at high pressure

The elemental antiferromagnet Cr at high pressure presents a new type of naked quantum critical point that is free of disorder and symmetry-breaking fields. Here we measure magnetotransport in fine detail around the critical pressure, Pc approximately 10 GPa, in a diamond anvil cell and reveal the role of quantum critical fluctuations at the phase transition. As the magnetism disappears and T-->0, the magnetotransport scaling converges to a non-mean-field form that illustrates the reconstruction of the magnetic Fermi surface, and is distinct from the critical scaling measured in chemically disordered CrV under pressure. The breakdown of itinerant antiferromagnetism only comes clearly into view in the clean limit, establishing disorder as a relevant variable at a quantum phase transition.

Observation of a two-dimensional fermi gas of atoms

We have prepared a degenerate gas of fermionic atoms which move in two dimensions while the motion in the third dimension is "frozen" by tight confinement and low temperature. In situ imaging provides direct measurement of the density profile and temperature. The gas is confined in a defect-free optical potential, and the interactions are widely tunable by means of a Fano-Feshbach resonance. This system can be a starting point for exploration of 2D Fermi physics and critical phenomena in a pure, controllable environment.

Doping effects in the coupled, two-leg spin ladder BiCu(2)PO(6)

We report preparation, x-ray diffraction, magnetic susceptibility χ(T) and heat capacity C(p)(T) measurements on undoped samples as well as samples with Zn-doped (S = 0) at the Cu site BiCu(2(1-x))Zn(2x)PO(6), Ni-doped (S = 1) at the Cu site BiCu(2(1-y))Ni(2y)PO(6), and Ca doped (holes) at the Bi site Bi(1-z)Ca(z)Cu(2)PO(6) in the coupled two-leg spin ladder system BiCu(2)PO(6). While, Zn shows complete solid solubility, Ni could be doped to about 20% and Ca to about 15%. Magnetization and heat capacity data in the undoped compound point towards the existence of frustration effects. In all the samples, the χ(T) at low temperature increases with doping content. The Zn-induced susceptibility is smaller than that due to effective S = 1/2 moments, possibly due to frustrating next-nearest-neighbor interactions along the leg. For Zn content x>0.01, χ(T) deviates from the Curie law at low temperatures. The magnetic specific heat data C(m)(T) for the Zn-doped samples show weak anomalies at low temperature, in agreement with the χ(T) behavior. The anomalies are suggestive of spin freezing at low- T. In contrast, prominent effects are observed in χ(T) and C(m)(T) on Ni-doped samples. The zero-field-cooled (ZFC) and field-cooled (FC) χ(T) data are different from each other at low temperature, unlike that for Zn-doped samples, clearly indicating a transition to a spin-glass-like phase. No anomalies were found in Ca- or Pb-doped samples.