Wigner crystal in one dimension

Observations of Charge-Density-Wave States in W6Te6 Wires

Determining the electronic ground state of a one-dimensional system is crucial to understanding the underlying physics of electronic behavior. Here, we demonstrate the discovery of charge-density wave states in few-wire W6Te6 arrays using scanning tunneling microscopy/spectroscopy. We directly visualize incommensurate charge orders, energy gaps with prominent coherence peaks, and the picometer-scale lattice distortion in nearly disorder-free double-wire systems, thereby demonstrating the existence of Peierls-type charge density waves. In the presence of disorder-induced charge order fluctuations, the coherence peaks resulting from phase correlation disappear and gradually transform the system into the pseudogap states. The power-law zero-bias anomaly and quasi-particle interference analysis further suggest the Tomonaga-Luttinger liquid behavior in such pseudogap region. In addition, we explicitly determined the evolution of the CDW energy gap as a function of stacking-wire numbers. The present study demonstrates the existence of electron-phonon interactions in few-wire W6Te6 that can be tuned by disorders and van der Waals stacking.

The Bulk van der Waals Layered Magnet CrSBr is a Quasi-1D Material

Correlated quantum phenomena in one-dimensional (1D) systems that exhibit competing electronic and magnetic order are of strong interest for the study of fundamental interactions and excitations, such as Tomonaga-Luttinger liquids and topological orders and defects with properties completely different from the quasiparticles expected in their higher-dimensional counterparts. However, clean 1D electronic systems are difficult to realize experimentally, particularly for magnetically ordered systems. Here, we show that the van der Waals layered magnetic semiconductor CrSBr behaves like a quasi-1D material embedded in a magnetically ordered environment. The strong 1D electronic character originates from the Cr-S chains and the combination of weak interlayer hybridization and anisotropy in effective mass and dielectric screening, with an effective electron mass ratio of m_X^e/m_Y^e ∼ 50. This extreme anisotropy experimentally manifests in strong electron-phonon and exciton-phonon interactions, a Peierls-like structural instability, and a Fano resonance from a van Hove singularity of similar strength to that of metallic carbon nanotubes. Moreover, because of the reduced dimensionality and interlayer coupling, CrSBr hosts spectrally narrow (1 meV) excitons of high binding energy and oscillator strength that inherit the 1D character. Overall, CrSBr is best understood as a stack of weakly hybridized monolayers and appears to be an experimentally attractive candidate for the study of exotic exciton and 1D-correlated many-body physics in the presence of magnetic order.

Emergence of Wigner oscillations in a model of real time cooling process: a time-dependent density-functional theory approach

Friedel and Wigner oscillations are well known phenomena occurring in quantum systems. Specifically, in a system composed byNconfined fermions, the former are characterized by the presence ofN/2peaks in the density distributions, whereas the last byNpeaks. Here, we considerN = 2 fermions harmonically confined in one-dimensional quantum dots. It is known that the transition from the Friedel to the Wigner oscillations is induced by the increment of interaction between the fermions. The increment of temperature, on the other hand, acts on eliminating the oscillations. In this context, by employing a time-dependent density-functional theory formalism, we here obtain the emergence of Wigner oscillations in a model which simulates a real time cooling process.

Asymmetric Wigner molecules in nanowire Y-junctions

The possibility of crystalline states of interacting electrons, known as Wigner crystals, has been intensively studied in each of the three dimensions. One-dimensional (1D) systems, however, can be interconnected forming two-dimensional (2D) lattices, being a three-terminal Y-junction (Y-J) the simplest one. Then, even when electrons in the individual branches of the Y are confined in 1D, as the Y-J is in 2D, one could expect significant differences in the crystalline state of the electron gas in a Y-J. With the recent report of fabrication of defect-free GaAs/AlGaAs Y-Js by epitaxial methods, the study of semiconductor Y-Js acquires a special relevance due to its eventual direct exploration. Here, by considering the collective electron interactions using a Yukawa-like effective potential, we explore a two-electron distribution in nanowire Y-Js by modulating its electron density via a screening parameter. We find that the electrons changes from a quasi-continuous to a Wigner molecule-like distribution when the electron density decreases in the Y-J. In bold contrast to the strict 1D case, where equidistant distributions of equal density are obtained in the Wigner regime, in the Y-J equidistant distributions of asymmetric density are induced. We also explore the effect of an external electric field acting along the Y-axis on the asymmetric distributions.

Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer

The famous, yet unsolved, Fermi-Hubbard model for strongly-correlated electronic systems is a prominent target for quantum computers. However, accurately representing the Fermi-Hubbard ground state for large instances may be beyond the reach of near-term quantum hardware. Here we show experimentally that an efficient, low-depth variational quantum algorithm with few parameters can reproduce important qualitative features of medium-size instances of the Fermi-Hubbard model. We address 1 × 8 and 2 × 4 instances on 16 qubits on a superconducting quantum processor, substantially larger than previous work based on less scalable compression techniques, and going beyond the family of 1D Fermi-Hubbard instances, which are solvable classically. Consistent with predictions for the ground state, we observe the onset of the metal-insulator transition and Friedel oscillations in 1D, and antiferromagnetic order in both 1D and 2D. We use a variety of error-mitigation techniques, including symmetries of the Fermi-Hubbard model and a recently developed technique tailored to simulating fermionic systems. We also introduce a new variational optimisation algorithm based on iterative Bayesian updates of a local surrogate model.

Suspended semiconductor nanostructures: physics and technology

The current state of research on quantum and ballistic electron transport in semiconductor nanostructures with a two-dimensional electron gas separated from the substrate and nanoelectromechanical systems is reviewed. These nanostructures fabricated using the surface nanomachining technique have certain unexpected features in comparison to their non-suspended counterparts, such as additional mechanical degrees of freedom, enhanced electron-electron interaction and weak heat sink. Moreover, their mechanical functionality can be used as an additional tool for studying the electron transport, complementary to the ordinary electrical measurements. The article includes a comprehensive review of spin-dependent electron transport and multichannel effects in suspended quantum point contacts, ballistic and adiabatic transport in suspended nanostructures, as well as investigations on nanoelectromechanical systems. We aim to provide an overview of the state-of-the-art in suspended semiconductor nanostructures and their applications in nanoelectronics, spintronics and emerging quantum technologies.

Tunneling between parallel one-dimensional Wigner crystals

Vertically aligned arrays are a frequent outcome in the nanowires synthesis by self-assembly techniques or in its subsequent processing. When these nanowires are close enough, quantum electron tunneling is expected between them. Then, because extended or localized electronic states can be established in the wires by tuning its electron density, the tunneling configuration between adjacent wires could be conveniently adjusted by an external gate. In this contribution, by considering the collective nature of electrons using a Yukawa-like effective potential, we explore the electron interaction between closely spaced, parallel nanowires while varying the electron density and geometrical parameters. We find that, at a low-density Wigner crystal regime, the tunneling can take place between adjacent localized states along and transversal to the wires axis, which in turn allows to create two- and three-dimensional electronic distributions with valuable potential applications.

Nanoscale Control of One-Dimensional Confined States in Strongly Correlated Homojunctions

Construction of lateral junctions is essential to generate one-dimensional (1D) confined potentials that can effectively trap quasiparticles. A series of remarkable electronic phases in one dimension, such as Wigner crystallization, are expected to be realized in such junctions. Here, we demonstrate that we can precisely tune the 1D-confined potential with an in situ manipulation technique, thus providing a dynamic way to modify the correlated electronic states at the junctions. We confirm the existence of 1D-confined potential at the homojunction of two single-layer 1T-NbSe₂ islands. Such potential is structurally sensitive and shows a nonmonotonic function of their interspacing. Moreover, there is a change of electronic properties from the correlated insulator to the generalized 1D Wigner crystallization while the confinement becomes strong. Our findings not only establish the capability to fabricate structures with dynamically tunable properties, but also pave the way toward more exotic correlated systems in low dimensions.

Wigner solids of domain wall skyrmions

Detection and characterization of a different type of topological excitations, namely the domain wall (DW) skyrmion, has received increasing attention because the DW is ubiquitous from condensed matter to particle physics and cosmology. Here we present experimental evidence for the DW skyrmion as the ground state stabilized by long-range Coulomb interactions in a quantum Hall ferromagnet. We develop an alternative approach using nonlocal resistance measurements together with a local NMR probe to measure the effect of low current-induced dynamic nuclear polarization and thus to characterize the DW under equilibrium conditions. The dependence of nuclear spin relaxation in the DW on temperature, filling factor, quasiparticle localization, and effective magnetic fields allows us to interpret this ground state and its possible phase transitions in terms of Wigner solids of the DW skyrmion. These results demonstrate the importance of studying the intrinsic properties of quantum states that has been largely overlooked.

Skyrmions, a topological spin texture, have been found in a variety of magnetic systems, including quantum hall ferromagnets. Here, Yang et al demonstrate the existence of skyrmions in domain walls in a quantum Hall ferromagnet, and suggest that these skyrmions form a 1D Wigner crystal.

Locally commensurate charge-density wave with three-unit-cell periodicity in YBa2Cu3Oy

In order to identify the mechanism responsible for the formation of charge-density waves (CDW) in cuprate superconductors, it is important to understand which aspects of the CDW's microscopic structure are generic and which are material-dependent. Here, we show that, at the local scale probed by NMR, long-range CDW order in YBa2Cu3Oy is unidirectional with a commensurate period of three unit cells (λ = 3b), implying that the incommensurability found in X-ray scattering is ensured by phase slips (discommensurations). Furthermore, NMR spectra reveal a predominant oxygen character of the CDW with an out-of-phase relationship between certain lattice sites but no specific signature of a secondary CDW with λ = 6b associated with a putative pair-density wave. These results shed light on universal aspects of the cuprate CDW. In particular, its spatial profile appears to generically result from the interplay between an incommensurate tendency at long length scales, possibly related to properties of the Fermi surface, and local commensuration effects, due to electron-electron interactions or lock-in to the lattice.

Many-Body Physics in Small Systems: Observing the Onset and Saturation of Correlation in Linear Atomic Chains

The exact study of small systems can guide us toward relevant measures for extracting information about many-body physics as we move to larger and more complex systems capable of quantum information processing or quantum analog simulation. We use exact diagonalization to study many electrons in short 1-D atom chains represented by long-range extended Hubbard-like models. We introduce a novel measure, the Single-Particle Excitation Content (SPEC) of an eigenstate and show that the dependence of SPEC on eigenstate number reveals the nature of the ground state (ordered phases), and the onset and saturation of correlation between the electrons as Coulomb interaction strength increases. We use this SPEC behavior to identify five regimes as interaction is increased: a non-interacting single-particle regime, a regime of perturbative Coulomb interaction in which the SPEC is a nearly universal function of eigenstate number, the onset and saturation of correlation, a regime of fully correlated states in which hopping is a perturbation and SPEC is a different universal function of state number, and the regime of no hopping. In particular, the behavior of the SPEC shows that when electron-electron correlation plays a minor role, all of the lowest energy eigenstates are made up primarily of single-particle excitations of the ground state, and as the Coulomb interaction increases, the lowest energy eigenstates increasingly contain many-particle excitations. In addition, the SPEC highlights a fundamental, distinct difference between a non-interacting system and one with minute, very weak interactions. While SPEC is a quantity that can be calculated for small exactly diagonalizable systems, it guides our intuition for larger systems, suggesting the nature of excitations and their distribution in the spectrum. Thus, this function, like correlation functions or order parameters, provides us with a window of intuition about the behavior of a physical system.

Non-Fermi Liquids in Conducting Two-Dimensional Networks

We explore the physics of novel fermion liquids emerging from conducting networks, where 1D metallic wires form a periodic 2D superstructure. Such structure naturally appears in marginally twisted bilayer graphenes, moire transition metal dichalcogenides, and also in some charge-density wave materials. For these network systems, we theoretically show that a remarkably wide variety of new non-Fermi liquids emerge and that these non-Fermi liquids can be classified by the characteristics of the junctions in networks. Using this, we calculate the electric conductivity of the non-Fermi liquids as a function of temperature, which show markedly different scaling behaviors than a regular 2D Fermi liquid.

A Short Review of One-Dimensional Wigner Crystallization

The simplest possible structural transition that an electronic system can undergo is Wigner crystallization. The aim of this short review is to discuss the main aspects of three recent experimets on the one-dimensional Wigner molecule, starting from scratch. To achieve this task, the Luttinger liquid theory of weakly and strongly interacting fermions is briefly addressed, together with the basic properties of carbon nanotubes that are required. Then, the most relevant properties of Wigner molecules are addressed, and finally the experiments are described. The main physical points that are addressed are the suppression of the energy scales related to the spin and isospin sectors of the Hamiltonian, and the peculiar structure that the electron density acquires in the Wigner molecule regime.

Mott-Glass Phase of a One-Dimensional Quantum Fluid with Long-Range Interactions

We investigate the ground-state properties of quantum particles interacting via a long-range repulsive potential V_{σ}(x)∼1/|x|^{1+σ} (-1<σ) or V_{σ}(x)∼-|x|^{-1-σ} (-2≤σ<-1) that interpolates between the Coulomb potential V_{0}(x) and the linearly confining potential V_{-2}(x) of the Schwinger model. In the absence of disorder the ground state is a Wigner crystal when σ≤0. Using bosonization and the nonperturbative functional renormalization group we show that any amount of disorder suppresses the Wigner crystallization when -3/2<σ≤0; the ground state is then a Mott glass, i.e., a state that has a vanishing compressibility and a gapless optical conductivity. For σ<-3/2 the ground state remains a Wigner crystal.

Dynamic correlation effects on correlational properties of finite-temperature quasi-one-dimensional electron gas

We have studied correlational properties of quasi-one-dimensional electron gas at finite temperatureTby incorporating the dynamics of electron correlations within the quantum version of the self-consistent mean-field approach of Singwi, Tosi, Land, and Sjölander. Static structure factor, pair-correlation function, static density susceptibility, excess kinetic energy, and free correlation energy are calculated covering a wide range of temperature and electron number density. As at absolute zero temperature, the inclusion of dynamics of correlations results in stronger spatial electron correlations, with a pronounced peak in the static structure factor at wave vectorq∼ 3.5kF, which grows further with decreasing electron density. Below a critical density, the static density susceptibility seems to diverge at this value ofq, signaling a transition from liquid to the Wigner crystal state-a prediction in qualitative agreement with recent simulations and experiment. However, thermal effects tend to impede crystallization with the consequence that the critical density decreases significantly with risingT. On the other hand, the pair-correlation function at short range exhibits a non-monotonic dependence onT, initially becoming somewhat stronger with risingTand then weakening continuously above a sufficiently highT. The calculated free correlation energy shows a noticeable dependence onT, with its magnitude increasing with increase inT. Further, we have looked into the effect of temperature on the frequency-dependence of dynamic local-field correction factor and the plasmon dispersion. It is found that with risingTthe dynamics of correlations weakens, and the plasmon frequency exhibits a blue shift. Wherever interesting, we have compared our results with the lower-order approximate calculations and zero-Tquantum Monte Carlo simulations.

Ground states of long-range interacting fermions in one spatial dimension

We systematically explore the ground state properties of one dimensional fermions with long-range interactions decaying in a power law  ∼[Formula: see text] through the density matrix renormalization group algorithm. By comparing values of Luttinger liquid parameters precisely measured in two different ways, we show convincing evidence that Luttinger liquid theory is valid if [Formula: see text] is larger than some threshold, otherwise the theory breaks down. Combining analysis on structure factor, charge gap and charge stiffness, we determine how the metal-insulator transition point develops as the interaction range is continuously tuned. A region in the range of [Formula: see text] has small interactions and finite charge gaps, but, interestingly, it shows metallic nature at the same time. We obtain approximate phase diagrams for the entire parameter space and for band fillings equal to 1/2 and 1/3. Finally, we compare certain bosonization and field theory formulas with our quasi-exact numerical results, from which disagreements are found.

Imaging the electronic Wigner crystal in one dimension

The quantum crystal of electrons, predicted more than 80 years ago by Eugene Wigner, remains one of the most elusive states of matter. In this study, we observed the one-dimensional Wigner crystal directly by imaging its charge density in real space. To image, with minimal invasiveness, the many-body electronic density of a carbon nanotube, we used another nanotube as a scanning-charge perturbation. The images we obtained of a few electrons confined in one dimension match the theoretical predictions for strongly interacting crystals. The quantum nature of the crystal emerges in the observed collective tunneling through a potential barrier. These experiments provide the direct evidence for the formation of small Wigner crystals and open the way for studying other fragile interacting states by imaging their many-body density in real space.

How adsorbates alter the metallic behavior of quasi-1D electron systems of the Si(5 5 3)-Au surface

The plasmonic signals of quasi-1D electron systems are a clear and direct measure of their metallic behavior. Due to the finite size of such systems in reality, plasmonic signals from a gold-induced superstructure on Si(5 5 3) can be studied with infrared spectroscopy. The infrared spectroscopic features have turned out to be extremely sensitive to adsorbates. Even without geometrical changes of the surface superstructure, the effects of doping, of the adsorbate induced electronic surface scattering, and of the electronic polarizability changes on top of the substrate surface give rise to measurable changes of the plasmonic signal. Especially strong changes of the plasmonic signal have been observed for gold, oxygen, and hydrogen exposure. The plasmonic resonance gradually disappears under these exposures, indicating the transion to an insulating behavior, which is in accordance with published results obtained from other experimental methods. For C₇₀ and, as shown here for the first time, TAPP-Br, the plasmonic signal almost retains its original intensity even up to coverages of many monolayers. For C₇₀, the changes of the spectral shape, e.g. of electronic damping and of the resonance position, were also found to be marginal. On the other hand, TAPP-Br adsorption shifts the plasmonic resonance to higher frequencies and strongly increases the electronic damping. Given the dispersion relation for plasmonic resonances of 1D electron systems, the findings for TAPP-Br indicate a push-back effect and therefore stronger confinement of the free charge carriers in the quasi-one-dimensonal channel due to the coverage by the flat TAPP-Br molecules. On the gold-doped Si(5 5 3)-Au surface TAPP-Br acts as counter dopant and increases the plasmonic signal.

Stability of charged density waves in InAs nanowires in an external magnetic field

We report on magnetotransport measurements at [Formula: see text] K in a high-quality InAs nanowire ([Formula: see text] kΩ) in the presence of the charged tip of an atomic force microscope serving as a mobile gate. We demonstrate the crucial role of the external magnetic field on the amplitude of the charge density waves with a wavelength of 0.8 μm. The observed suppression rate of their amplitude is similar or slightly higher than the one for weak localization correction in our investigated InAs nanowire.

Carbon nanotubes as excitonic insulators

Fifty years ago Walter Kohn speculated that a zero-gap semiconductor might be unstable against the spontaneous generation of excitons–electron–hole pairs bound together by Coulomb attraction. The reconstructed ground state would then open a gap breaking the symmetry of the underlying lattice, a genuine consequence of electronic correlations. Here we show that this excitonic insulator is realized in zero-gap carbon nanotubes by performing first-principles calculations through many-body perturbation theory as well as quantum Monte Carlo. The excitonic order modulates the charge between the two carbon sublattices opening an experimentally observable gap, which scales as the inverse of the tube radius and weakly depends on the axial magnetic field. Our findings call into question the Luttinger liquid paradigm for nanotubes and provide tests to experimentally discriminate between excitonic and Mott insulators.

It has long been anticipated theoretically that semiconductors with small band gaps may form a correlated exciton insulator phase, but it has been difficult to find material realisations. Here, the authors predict numerically that zero-gap armchair carbon nanotubes could be exciton insulators.

True Bilayer Exciton Condensate of One-Dimensional Electrons

We theoretically predict that a true bilayer exciton condensate, characterized by off-diagonal long-range order and global phase coherence, can be created in one-dimensional solid state electron systems. The mechanism by which this happens is to introduce a single particle hybridization of electron and hole populations, which locks the phase of the relevant mode and hence invalidates the Mermin-Wagner theorem. Electron-hole interactions then amplify this tendency towards off-diagonal long-range order, enhancing the condensate properties by more than an order of magnitude over the noninteracting limit. We show that the temperatures below which a substantial condensate fraction would form could reach hundreds of Kelvin, a benefit of the weak screening in one-dimensional systems.

Fractional Wigner Crystal in the Helical Luttinger Liquid

The properties of the strongly interacting edge states of two dimensional topological insulators in the presence of two-particle backscattering are investigated. We find an anomalous behavior of the density-density correlation functions, which show oscillations that are neither of Friedel nor of Wigner type: they, instead, represent a Wigner crystal of fermions of fractional charge e/2, with e the electron charge. By studying the Fermi operator, we demonstrate that the state characterized by such fractional oscillations still bears the signatures of spin-momentum locking. Finally, we compare the spin-spin correlation functions and the density-density correlation functions to argue that the fractional Wigner crystal is characterized by a nontrivial spin texture.

Current noise as a probe for Wigner molecules

The effects of a Wigner molecule on the current noise and conductance of a one-dimensional quantum dot with two electrons are investigated. Focusing on a lateral transport setup, the sequential regime is considered. Tunnelling rates through the dot are evaluated within an exact diagonalisation scheme. They strongly depend on electron interactions, showing a markedly different behaviour in the presence of a Wigner molecule with respect to the weak interactions case, and thus modify the transport and current noise and the dot. For weak interactions negative differential conductance and super-Poissonian noise are found. As interactions increase, a Wigner molecule develops: it suppresses the negative differential conductance and turns the shot noise to sub-Poissonian values. In particular, the noise is found to be a sensitive probe of the Wigner molecule.

Thermally enhanced Wigner oscillations in two-electron 1D quantum dots

Motivated by a recent experiment (Pecker et al 2013 Nat. Phys. 9 576), we study the stability, with respect to thermal effects, of Friedel and Wigner density fluctuations for two electrons trapped in a one-dimensional quantum dot. Diagonalizing the system exactly, the finite-temperature average electron density is computed. While the weak and strong interaction regimes display a Friedel oscillation or a Wigner molecule state at zero temperature, which as expected smear and melt as the temperature increases, a peculiar thermal enhancement of Wigner correlations in the intermediate interaction regime is found. We demonstrate that this effect is due to the presence of two different characteristic temperature scales: T(F), dictating the smearing of Friedel oscillations, and T(W), smoothing Wigner oscillations. In the early Wigner molecule regime, for intermediate interactions, T(F) < T(W) leading to the enhancement of the visibility of Wigner oscillations. These results complement those obtained within the Luttinger liquid picture, valid for larger numbers of particles.

Wigner crystallization of single photons in cold Rydberg ensembles

The coupling of weak light fields to Rydberg states of atoms under conditions of electromagnetically induced transparency leads to the formation of Rydberg polaritons which are quasiparticles with tunable effective mass and nonlocal interactions. Confined to one spatial dimension their low energy physics is that of a moving-frame Luttinger liquid which, due to the nonlocal character of the repulsive interaction, can form a Wigner crystal of individual photons. We calculate the Luttinger K parameter using density-matrix renormalization group simulations and find that under typical slow-light conditions kinetic energy contributions are too strong for crystal formation. However, adiabatically increasing the polariton mass by turning a light pulse into stationary spin excitations allows us to generate true crystalline order over a finite length. The dynamics of this process and asymptotic correlations are analyzed in terms of a time-dependent Luttinger theory.

Probing Wigner correlations in a suspended carbon nanotube

The influence of electron–vibron coupling on the transport properties of a strongly interacting quantum dot built in a suspended carbon nanotube (CNT) is analyzed. The latter is probed by a charged atomic force microscope tip scanned along the axis of the CNT which induces oscillations of the chemical potential and of the linear conductance. These oscillations are due to the competition between finite-size effects and the formation of a Wigner molecule for strong interactions. Such oscillations are shown to be suppressed by the electron–vibron coupling. The suppression is more pronounced in the regime of weak Coulomb interactions, which ensures that probing Wigner correlations in such a system is in principle possible.

Zigzag phase transition in quantum wires

We study the quantum phase transition of interacting electrons in quantum wires from a one-dimensional (1D) linear configuration to a quasi-1D zigzag arrangement using quantum Monte Carlo methods. As the density increases from its lowest values, first, the electrons form a linear Wigner crystal, then, the symmetry about the axis of the wire is broken as the electrons order in a quasi-1D zigzag phase, and, finally, the electrons form a disordered liquidlike phase. We show that the linear to zigzag phase transition is not destroyed by the strong quantum fluctuations present in narrow wires; it has characteristics which are qualitatively different from the classical transition.

Correlation effects in two-dimensional topological insulators

Topological insulators have become one of the most active research areas in condensed matter physics. This article reviews progress on the topic of electronic correlation effects in the two-dimensional case, with a focus on systems with intrinsic spin-orbit coupling and numerical results. Topics addressed include an introduction to the noninteracting case, an overview of theoretical models, correlated topological band insulators, interaction-driven phase transitions, topological Mott insulators and fractional topological states, correlation effects on helical edge states, and topological invariants of interacting systems.

Wigner crystal versus fermionization for one-dimensional Hubbard models with and without long-range interactions

The ground state properties of the Hubbard model with or without long-range interactions in the regime with strongly repulsive on-site interactions are investigated by means of the exact diagonalization method. We show that the appearance of N-crests in the density profile of a trapped N-fermion system is a natural result of 'fermionization' between antiparallel-spin fermions in the strongly repulsive limit and cannot be taken as the only signature of the Wigner crystal phase, as the static structure factor does not show any signature of crystallization. In contrast, both the density distribution and the static structure factor of the Hubbard model with strong long-range interactions display clear signatures of the Wigner crystal phase. Our results indicate the important role of long-range interaction in the formation of the Wigner crystal phase.

Topological Wigner crystal of half-solitons in a spinor Bose-Einstein condensate

We consider a one-dimensional gas of half-solitons in a spinor Bose-Einstein condensate. We calculate the topological interaction potential between the half-solitons. Using a kinetic equation of the Vlasov-Boltzmann type, we model the coupled dynamics of the interacting solitons. We show that the dynamics of the system in the gaseous phase is marginally stable and spontaneously evolves toward a Wigner crystal.

Physics in one dimension: theoretical concepts for quantum many-body systems

Various sophisticated approximation methods exist for the description of quantum many-body systems. It was realized early on that the theoretical description can simplify considerably in one-dimensional systems and various exact solutions exist. The focus in this introductory paper is on fermionic systems and the emergence of the Luttinger liquid concept.

Thermalization of acoustic excitations in a strongly interacting one-dimensional quantum liquid

We study inelastic decay of bosonic excitations in a Luttinger liquid. In a model with a linear excitation spectrum the decay rate diverges. We show that this difficulty is resolved when the interaction between constituent particles is strong, and the excitation spectrum is nonlinear. Although at low energies the nonlinearity is weak, it regularizes the divergence in the decay rate. We develop a theoretical description of the approach of the system to thermal equilibrium. The typical relaxation rate scales as the fifth power of temperature.

Non-linear Coulomb blockade microscopy of a correlated one-dimensional quantum dot

We evaluate the chemical potential of a one-dimensional quantum dot coupled to an atomic force microscope tip. The dot is described within the Luttinger liquid framework, and the conductance peak positions as a function of the tip location are calculated in the linear and non-linear transport regimes for an arbitrary number of particles. The differences between the chemical potential oscillations induced by the Friedel and Wigner terms are carefully analysed in the whole range of interaction strengths. It is shown that Friedel oscillations, unlike the Wigner ones, are sensitive probes for detecting excited spin states and collective spin density waves involved in the transport.

How a single stretched polymer responds coherently to a minute oscillation in fluctuating environments: an entropic stochastic resonance

Within the cell, biopolymers are often situated in constrained, fluid environments, e.g., cytoskeletal networks, stretched DNAs in chromatin. It is of paramount importance to understand quantitatively how they, utilizing their flexibility, optimally respond to a minute signal, which is, in general, temporally fluctuating far away from equilibrium. To this end, we analytically study viscoelastic response and associated stochastic resonance in a stretched single semi-flexible chain to an oscillatory force or electric field. Including hydrodynamic interactions between chain segments, we evaluate dynamics of the polymer extension in coherent response to the force or field. We find power amplification factor of the response at a noise-strength (temperature) can attain the maximum that grows as the chain length increases, indicative of an entropic stochastic resonance (ESR). In particular for a charged chain under an electric field, we find that the maximum also occurs at an optimal chain length, a new feature of ESR. The hydrodynamic interaction is found to enhance the power amplification, representing unique polymer cooperativity which the fluid background imparts despite its overdamping nature. For the slow oscillatory force, the resonance behavior is explained by the chain undulation of the longest wavelength. This novel ESR phenomenon suggests how a biopolymer self-organizes in an overdamping environment, utilizing its flexibility and thermal fluctuations.

Insulating state and breakdown of Fermi liquid description in molecular-scale single-crystalline wires of gold

Electrical transport measurements on ultrathin single-crystalline Au nanowires, synthesized via a wet chemical route, show an unexpected insulating behavior. The linear response electrical resistance exhibits a power-law dependence on temperature. In addition, the variation of current over a wide range of temperature and voltage obeys a universal scaling relation that provides compelling evidence for a non-Fermi liquid behavior. Our results demonstrate that the quantum ground state in ultrathin nanowires of simple metallic systems can be radically different from their bulk counterparts and can be described in terms of a Tomonaga-Luttinger liquid (TLL), in the presence of remarkably strong electron-electron interactions.

Positive and negative drag, dynamic phases, and commensurability in coupled one-dimensional channels of particles with Yukawa interactions

We introduce a simple model consisting of two or three coupled one-dimensional channels of particles with Yukawa interactions. For the two-channel system, when an external drive is applied only to the top or primary channel, we find a transition from locked flow, where particles in both channels move together, to decoupled flow, where the particles in the secondary or undriven channel move at a slower velocity than the particles in the primary or driven channel. Pronounced commensurability effects in the decoupling transition occur when the ratio of the number of particles in the top and bottom channels is varied, and the coupling of the two channels is enhanced when this ratio is an integer or a rational fraction. Near the commensurate fillings, we find additional features in the velocity-force curves caused by the slipping of individual vacancies or incommensurations in the secondary channels. For three coupled channels, when only the top channel is driven we find a remarkably rich variety of distinct dynamic phases, including multiple decoupling and recoupling transitions. These transitions produce pronounced signatures in the velocity response of each channel. We also find regimes where a negative drag effect can be induced in one of the nondriven channels. The particles in this channel move in the opposite direction from the particles in the driven channel due to the mixing of the two different periodic frequencies produced by the discrete motion of the particles in the two other channels. In the two-channel system, we also demonstrate a ratchet effect for the particles in the secondary channel when an asymmetric drive is applied to the primary channel. This ratchet effect is similar to that observed in superconducting vortex systems when there is a coupling between two different species of vortices.

Dirac's method for constraints: an application to quantum wires

We investigate the Hubbard model in the limit U = ∞, which is equivalent to the statistical condition of exclusion of double occupancy. We solve this problem using Dirac's method for constraints. The constraints are solved within the bosonization method. We find that the constraints modify the anomalous commutator. We apply this theory to quantum wires at finite temperatures where the Hubbard interaction is U = ∞. We find that the anomalous commutator induced by the constraints gives rise to the 0.7 anomalous conductance.

Quantum zigzag transition in ion chains

A string of trapped ions at zero temperature exhibits a structural phase transition to a zigzag structure, tuned by reducing the transverse trap potential or the interparticle distance. The transition is driven by transverse, short wavelength vibrational modes. We argue that this is a quantum phase transition, which can be experimentally realized and probed. Indeed, by means of a mapping to the Ising model in a transverse field, we estimate the quantum critical point in terms of the system parameters, and find a finite, measurable deviation from the critical point predicted by the classical theory. A measurement procedure is suggested which can probe the effects of quantum fluctuations at criticality. These results can be extended to describe the transverse instability of ultracold polar molecules in a one-dimensional optical lattice.

One-dimensional quantum liquids with power-law interactions: the Luttinger staircase

We study one-dimensional fermionic and bosonic gases with repulsive power-law interactions 1/|x|(β), with β>1, in the framework of Tomonaga-Luttinger liquid (TLL) theory. We obtain an accurate analytical expression linking the TLL parameter to the microscopic Hamiltonian, for arbitrary β and strength of the interactions. In the presence of a small periodic potential, power-law interactions make the TLL unstable towards the formation of a cascade of lattice solids with fractional filling, a "Luttinger staircase." Several of these quantum phases and phase transitions are realized with ground state polar molecules and weakly bound magnetic Feshbach molecules.

Equilibration of a one-dimensional Wigner crystal

Equilibration of a one-dimensional system of interacting electrons requires processes that change the numbers of left- and right-moving particles. At low temperatures such processes are strongly suppressed, resulting in slow relaxation towards equilibrium. We study this phenomenon in the case of spinless electrons with strong long-range repulsion, when the electrons form a one-dimensional Wigner crystal. We find the relaxation rate by accounting for the umklapp scattering of phonons in the crystal. For the integrable model of particles with inverse-square repulsion, the relaxation rate vanishes.

Vicious walks with long-range interactions

The asymptotic behavior of the survival or reunion probability of vicious walks with short-range interactions is generally well studied. In many realistic processes, however, walks interact with a long-ranged potential that decays in d dimensions with distance r as r(-d-σ). We employ methods of renormalized field theory to study the effect of such long-range interactions. We calculate the exponents describing the decay of the survival probability for all values of parameters σ and d to first order in the double expansion in ε=2-d and δ=2-d-σ. We show that there are several regions in the σ-d plane corresponding to different scalings for survival and reunion probabilities. Furthermore, we calculate the leading logarithmic corrections.

A scaling approach for interacting quantum wires--a possible explanation for the 0.7 anomalous conductance

We consider a weakly interacting finite wire with short and long range interactions. The long range interactions enhance the 4k(F) scattering and renormalize the wire to a strongly interacting limit. For large screening lengths, the renormalized charge stiffness Luttinger parameter K(eff) decreases to [Formula: see text], giving rise to a Wigner crystal at T=0 with an anomalous conductance at finite temperatures. For short screening lengths, the renormalized Luttinger parameter K(eff) is restricted to ½≤K(eff)≤1. As a result, at temperatures larger than the magnetic exchange energy we find an interacting metal which, for K(eff)≈½, is equivalent to the Hubbard U−>∞ model, with the anomalous conductance G≈e(2)/h.