Quantum Criticality of Two-Dimensional Quantum Magnets with Long-Range Interactions

Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions

Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.

Trapping Ion Coulomb Crystals in an Optical Lattice

We report the optical trapping of multiple ions localized at individual lattice sites of a one-dimensional optical lattice. We observe a fivefold increased range of axial dc-electric field strength for which ions can be optically trapped with high probability and an increase of the axial eigenfrequency by 2 orders of magnitude compared to an optical dipole trap without interference but of similar intensity. Our findings motivate an alternative pathway to extend arrays of trapped ions in size and dimension, enabling quantum simulations with particles interacting at long range.

Signatures of a Quantum Griffiths Phase Close to an Electronic Nematic Quantum Phase Transition

In the vicinity of a quantum critical point, quenched disorder can lead to a quantum Griffiths phase, accompanied by an exotic power-law scaling with a continuously varying dynamical exponent that diverges in the zero-temperature limit. Here, we investigate a nematic quantum critical point in the iron-based superconductor FeSe_{0.89}S_{0.11} using applied hydrostatic pressure. We report an unusual crossing of the magnetoresistivity isotherms in the nonsuperconducting normal state that features a continuously varying dynamical exponent over a large temperature range. We interpret our results in terms of a quantum Griffiths phase caused by nematic islands that result from the local distribution of Se and S atoms. At low temperatures, the Griffiths phase is masked by the emergence of a Fermi liquid phase due to a strong nematoelastic coupling and a Lifshitz transition that changes the topology of the Fermi surface.

Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms

Quantum simulation using synthetic systems is a promising route to solve outstanding quantum many-body problems in regimes where other approaches, including numerical ones, fail¹. Many platforms are being developed towards this goal, in particular based on trapped ions^2-4, superconducting circuits^5-7, neutral atoms^8-11 or molecules^12,13. All of these platforms face two key challenges: scaling up the ensemble size while retaining high-quality control over the parameters, and validating the outputs for these large systems. Here we use programmable arrays of individual atoms trapped in optical tweezers, with interactions controlled by laser excitation to Rydberg states¹¹, to implement an iconic many-body problem-the antiferromagnetic two-dimensional transverse-field Ising model. We push this platform to a regime with up to 196 atoms manipulated with high fidelity and probe the antiferromagnetic order by dynamically tuning the parameters of the Hamiltonian. We illustrate the versatility of our platform by exploring various system sizes on two qualitatively different geometries-square and triangular arrays. We obtain good agreement with numerical calculations up to a computationally feasible size (approximately 100 particles). This work demonstrates that our platform can be readily used to address open questions in many-body physics.

Frustration-induced supersolid phases of extended Bose-Hubbard model in the hard-core limit

We investigate exotic supersolid phases in the extended Bose-Hubbard model with infinite projected entangled-pair state, numerical exact diagonalization, and mean-field theory. We demonstrate that many different supersolid phases can be generated by changing signs of hopping terms, and the interactions along with the frustration of hopping terms are important to stabilize those supersolid states. We argue the effect of frustration introduced by the competition of hopping terms in the supersolid phases from the mean-field point of view. This helps to give a clearer picture of the background mechanism for underlying superfluid/supersolid states to be formed. With this knowledge, we predict and realize thed-wave superfluid, which shares the same pairing symmetry with high-Tcmaterials, and its extended phases. We believe that our results contribute to preliminary understanding for desired target phases in the real-world experimental systems.

Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4

Frustrated magnets hold the promise of material realizations of exotic phases of quantum matter, but direct comparisons of unbiased model calculations with experimental measurements remain very challenging. Here we design and implement a protocol of employing many-body computation methodologies for accurate model calculations—of both equilibrium and dynamical properties—for a frustrated rare-earth magnet TmMgGaO₄ (TMGO), which explains the corresponding experimental findings. Our results confirm TMGO is an ideal realization of triangular-lattice Ising model with an intrinsic transverse field. The magnetic order of TMGO is predicted to melt through two successive Kosterlitz–Thouless (KT) phase transitions, with a floating KT phase in between. The dynamical spectra calculated suggest remnant images of a vanishing magnetic stripe order that represent vortex–antivortex pairs, resembling rotons in a superfluid helium film. TMGO therefore constitutes a rare quantum magnet for realizing KT physics, and we further propose experimental detection of its intriguing properties.

TmMgGaO₄ is one of a number of recently-synthesized quantum magnets that are proposed to realize important theoretical models. Here the authors demonstrate the agreement between detailed experimental measurements and state-of-the-art predictions based on the 2D transverse-field triangular lattice Ising model.

Confined Quasiparticle Dynamics in Long-Range Interacting Quantum Spin Chains

We study the quasiparticle excitation and quench dynamics of the one-dimensional transverse-field Ising model with power-law (1/r^{α}) interactions. We find that long-range interactions give rise to a confining potential, which couples pairs of domain walls (kinks) into bound quasiparticles, analogous to mesonic states in high-energy physics. We show that these quasiparticles have signatures in the dynamics of order parameters following a global quench, and the Fourier spectrum of these order parameters can be exploited as a direct probe of the masses of the confined quasiparticles. We introduce a two-kink model to qualitatively explain the phenomenon of long-range-interaction-induced confinement and to quantitatively predict the masses of the bound quasiparticles. Furthermore, we illustrate that these quasiparticle states can lead to slow thermalization of one-point observables for certain initial states. Our work is readily applicable to current trapped-ion experiments.

Quantum Ising model on the frustrated square lattice

We investigate the role of a transverse field on the Ising square antiferromagnet with first (J_{1}) and second (J_{2}) neighbor interactions. Using a cluster mean-field approach, we provide a telltale characterization of the frustration effects on the phase boundaries and entropy accumulation process emerging from the interplay between quantum and thermal fluctuations. We found that the paramagnetic (PM) and antiferromagnetic phases are separated by continuous phase transitions. On the other hand, continuous and discontinuous phase transitions, as well as tricriticality, are observed in the phase boundaries between PM and superantiferromagnetic phases. A rich scenario arises when a discontinuous phase transition occurs in the classical limit while quantum fluctuations recover criticality. We also find that the entropy accumulation process predicted to occur at temperatures close to the quantum critical point can be enhanced by frustration. Our results provide a description for the phase boundaries and entropy behavior that can help to identify the ratio J_{2}/J_{1} in possible experimental realizations of the quantum J_{1}-J_{2} Ising antiferromagnet.