Luttinger Liquid Model Research Articles

Viscous flow in a one-dimensional spin-polarized Fermi gas: The role of integrability on viscosity

The transport properties of one-dimensional Fermi gases at low temperatures are often described by the Luttinger liquid (LL) model. However, to study dissipative effects, one needs to examine interactions beyond the LL model. In this work, we provide a simple model that allows for a direct microscopic calculation of the bulk viscosity, namely, the one-dimensional spin polarized $p$-wave Fermi gas. To leading order in the finite interaction strength, we find that the bulk viscosity is finite and consistent with the requirement of scale symmetry. We further show that the bulk viscosity satisfies the Bose-Fermi duality relating the weakly interacting limit of the spin polarized Fermi gas to the strongly interacting limit of the Lieb-Liniger model and vice versa. This work establishes the bulk viscosity to leading order in scale-breaking interactions in both the strongly and weakly interacting limits for both high and low temperatures.

Chiral Spin-Chain Interfaces Exhibiting Event-Horizon Physics.

The interface between different quantum phases of matter can give rise to novel physics, such as exotic topological phases or nonunitary conformal field theories. Here we investigate the interface between two spin chains in different chiral phases. Surprisingly, the mean field theory approximation of this interacting composite system is given in terms of Dirac fermions in a curved space-time geometry. In particular, the interface between the two phases represents a black hole horizon. We demonstrate that this representation is faithful both analytically, by employing bosonization to obtain a Luttinger liquid model, and numerically, by employing matrix product state methods. A striking prediction from the black hole equivalence emerges when a quench, at one side of the interface between two opposite chiralities, causes the other side to thermalize with the Hawking temperature for a wide range of parameters and initial conditions.

Crossed Luttinger liquid hidden in a quasi-two-dimensional material

Although the concept of Luttinger liquid (LL) that describes a one-dimensional (1D) interacting fermion system collapses in higher dimensions, it has been proposed to be closely related to many mysteries including the normal state of cuprate superconductor, unconventional metal, and quantum criticality. Therefore, the generalization of LL model to higher dimensions has attracted substantial research attention. Here we systematically investigate the electronic structure of a quasi-2D compound {\eta}-Mo4O11 using high-resolution angle-resolved photoemission spectroscopy and ab-initio calculation. Remarkably, we reveal a prototypical LL behavior originating from the crossing quasi-1D chain arrays hidden in the quasi-2D crystal structure. Our results suggest that {\eta}-Mo4O11 materializes the long sought-after crossed LL phase, where the orthogonal orbital components significantly reduce the coupling between intersecting quasi-1D chains and therefore maintain the essential properties of LL. Our finding not only presents a realization of 2D LL, but also provides a new angle to understand non-Fermi liquid behaviors in other 2D and 3D quantum materials.

Robustness of helical edge states under edge reconstruction

The helical edge states of time-reversal invariant two-dimensional topological insulators are protected against backscattering in idealized models. In more realistic scenarios with a shallow confining potential at the sample boundary, additional strongly interacting edge states may arise, that could interfere with the topological protection of edge conduction. We find that interaction effects within the reconstructed edges are well described by the Luttinger liquid model. While interactions between this Luttinger liquid and the helical edge states can in principle give rise to dynamical spin polarization and the breaking of time-reversal symmetry, we demonstrate that random spin-orbit coupling strongly suppresses such dynamical spin polarization, resulting in the persistence of near quantized edge conduction.

Tunneling maps of interacting electrons in real time: Anomalous tunneling in quantum point-contacts beyond the steady state regime

Strongly correlated transport of interacting electrons through the one-dimensional tunnel contact is considered within the Luttinger liquid model of one-dimensional electrodes on arbitrary time scales t>ħ/Λg. Using previous results, namely, the Self-equilibration theorem proven in Ref. [20] the exact distribution functions P(N,t) for the probabilities of N electrons to tunnel through the contact by the time t are derived and plotted as 3D intensity graphs called real-time tunneling maps in a whole available region of Luttinger liquid correlation parameter values, bias voltages, and temperatures. The tunneling maps being obtained reveal tunneling anomalies - unusually high tunneling probabilities for the small numbers of electrons on the short-time scales beyond the steady state regime of electron tunnel transport. Especially, this concerns the case of strong short-range electron-electron interaction in the leads at g≲1/2. The effect being found can be treated as the direct consequence of the self-equilibration phenomenon. It is shown that features of such an anomalous electron tunneling beyond the steady state regime can be used for precise experimental measurements of small differences between Luttinger liquid correlation parameter values in different one-dimensional quantum-point contacts.

One-dimensional Luttinger liquids in a two-dimensional moiré lattice.

The Luttinger liquid (LL) model of one-dimensional (1D) electronic systems provides a powerful tool for understanding strongly correlated physics, including phenomena such as spin-charge separation1. Substantial theoretical efforts have attempted to extend the LL phenomenology to two dimensions, especially in models of closely packed arrays of 1D quantum wires2-13, each being described as a LL. Such coupled-wire models have been successfully used to construct two-dimensional (2D) anisotropic non-Fermi liquids2-6, quantum Hall states7-9, topological phases10,11 and quantum spin liquids12,13. However, an experimental demonstration of high-quality arrays of 1D LLs suitable for realizing these models remains absent. Here we report the experimental realization of 2D arrays of 1D LLs with crystalline quality in a moiré superlattice made of twisted bilayer tungsten ditelluride (tWTe2). Originating from the anisotropic lattice of the monolayer, the moiré pattern of tWTe2 hosts identical, parallel 1D electronic channels, separated by a fixed nanoscale distance, which is tuneable by the interlayer twist angle. At a twist angle of approximately 5 degrees, we find that hole-doped tWTe2 exhibits exceptionally large transport anisotropy with a resistance ratio of around 1,000 between two orthogonal in-plane directions. The across-wire conductance exhibits power-law scaling behaviours, consistent with the formation of a 2D anisotropic phase that resembles an array of LLs. Our results open the door for realizing a variety of correlated and topological quantum phases based on coupled-wire models and LL physics.

Disorder-induced phase transitions in a spinful one-dimensional system

We analyse a modified set of renormalisation group equations for disordered spinful fermions described by the Luttinger liquid model. The modification is necessary to take special care of the factitious admixture of the disorder to the interaction coupling constants undergoing renormalisation. Only properly separated amplitudes of elastic and inelastic processes allow the identification of true phases and the construction of the phase diagram (a similar procedure has been earlier implemented for the spinless case). In the spinful case, these modified equations enable us to demonstrate that in some region of the bare parameters values the phase diagram contains two massive phases, charge (CDW) and spin (SDW) density waves, which are separated by an insulating phase. These gapped phases are achieved at finite critical temperatures that vanish at the phase boundaries indicating the presence of a disorder-induced quantum phase transition. The critical temperatures as a function of disorder are reasonably well fit by a stretch exponential with the universal stretching critical exponent ν=1/3. A quantum phase transition between CDW and SDW phases driven by disorder strength has not been predicted before and this observation must be taken into account when analysing recent multiple experiments on phase transitions in quasi-one-dimensional structures.

Kinetic Processes in Fermi–Luttinger Liquids

In this work we discuss extensions of the pioneering analysis by Dzyaloshinskii and Larkin of correlation functions for one-dimensional Fermi systems, focusing on the effects of quasiparticle relaxation enabled by a nonlinear dispersion. Throughout the work we employ both, the weakly interacting Fermi gas picture and nonlinear Luttinger liquid theory to describe attenuation of excitations and explore the fermion-boson duality between both approaches. Special attention is devoted to the role of spin-exchange processes, effects of interaction screening, and integrability. Thermalization rates for electron- and hole-like quasiparticles, as well as the decay rate of collective plasmon excitations and the momentum space mobility of spin excitations are calculated for various temperature regimes. The phenomenon of spin-charge drag is considered and the corresponding momentum transfer rate is determined. We further discuss how momentum relaxation due to several competing mechanisms, viz. triple electron collisions, electron-phonon scattering, and long-range inhomogeneities affect transport properties, and highlight energy transfer facilitated by plasmons from the perspective of the inhomogeneous Luttinger liquid model. Finally, we derive the full matrix of thermoelectric coefficients at the quantum critical point of the first conductance plateau transition, and address magnetoconductance in ballistic semiconductor nanowires with strong Rashba spin-orbit coupling.

A tied Fermi liquid to Luttinger liquid model for nonlinear transport in conducting polymers

Organic conjugated polymers demonstrate great potential in transistors, solar cells and light-emitting diodes, whose performances are fundamentally governed by charge transport. However, the morphology–property relationships and the underpinning charge transport mechanisms remain unclear. Particularly, whether the nonlinear charge transport in conducting polymers is appropriately formulated within non-Fermi liquids is not clear. In this work, via varying crystalline degrees of samples, we carry out systematic investigations on the charge transport nonlinearity in conducting polymers. Possible charge carriers’ dimensionality is discussed when varying the molecular chain’s crystalline orders. A heterogeneous-resistive-network (HRN) model is proposed based on the tied-link between Fermi liquids (FL) and Luttinger liquids (LL), related to the high-ordered crystalline zones and weak-coupled amorphous regions, respectively. The HRN model is supported by precise electrical and microstructural characterizations, together with theoretic evaluations, which well describes the nonlinear transport behaviors and provides new insights into the microstructure-correlated charge transport in organic solids.

KINETIC PROCESSES IN FERMI-LUTTINGER LIQUIDS

In this work we discuss extensions of the pioneering analysis by Dzyaloshinskii and Larkin of correlation functions for one-dimensional Fermi systems, focusing on the effects of quasiparticle relaxation enabled by a nonlinear dispersion. Throughout the work we employ both, the weakly interacting Fermi gas picture and nonlinear Luttinger liquid theory to describe attenuation of excitations and explore the fermion-boson duality between both approaches. Special attention is devoted to the role of spin-exchange processes, effects of interaction screening, and integrability. Thermalization rates for electron- and hole-like quasiparticles, as well as the decay rate of collective plasmon excitations and the momentum space mobility of spin excitations are calculated for various temperature regimes. The phenomenon of spin-charge drag is considered and the corresponding momentum transfer rate is determined. We further discuss how momentum relaxation due to several competing mechanisms, viz. triple electron collisions, electron-phonon scattering, and long-range inhomogeneities affect transport properties, and highlight energy transfer facilitated by plasmons from the perspective of the inhomogeneous Luttinger liquid model. Finally, we derive the full matrix of thermoelectric coefficients at the quantum critical point of the first conductance plateau transition, and address magnetoconductance in ballistic semiconductor nanowires with strong Rashba spin-orbit coupling.

Possible Thermodynamical Phase Slips in Superfluid 4He Confined in a 2.5-nm Channel of FSM

We have measured the superfluid response of 4He confined in a 2.5-nm channel and have compared with that of 4He in a 2.8-nm channel. In the 2.5-nm channel, the superfluid growth is gradual regardless of areal density and pressure. In contrast, 4He in a 2.8-nm channel shows a sharp superfluid onset at low pressure, although it shows a gradual temperature dependence with increasing pressure. The gradual temperature dependence in both channels is well fitted to the function of static superfluid density based on the Tomonaga–Luttinger liquid model. It indicates that the thermal excitation of phase slips plays an important role in the observed superfluid response.

Quantum Monte Carlo study of strongly interacting bosonic one-dimensional systems in periodic potentials

We present diffusion Monte Carlo (DMC) and path-integral Monte Carlo (PIMC) calculations of a one-dimensional Bose system with realistic interparticle interactions in a periodic external potential. Our main aim is to test the predictions of the Luttinger liquid (LL) theory, in particular with respect to the superfluid-Mott insulator transition at both zero and finite temperatures, in the predicted robust and fragile superfluid regimes. For that purpose, we present our results of the superfluid fraction $\rho_s/\rho_0$, the one-body density matrix, the two-body correlation functions, and the static structure factor. The DMC and PIMC results in the limit of very low temperature for $\rho_s/\rho_0$ agree, but the LL model for scaling $\rho_s/\rho_0$ does not fit the data well. The critical depth of the periodic potential is close to the values obtained for ultracold gases with different models of interaction, but with the same value of the bare LL parameter, demonstrating the universality of LL description. Algebraic decay of correlation functions is observed in the superfluid regime and exponential decay in the Mott-insulator one, as well as in all regimes at finite temperature for distances larger than a characteristic length.

From the moving piston to the dynamical Casimir effect: Explorations with shaken condensates

Recent experimental realizations of uniform confining potentials for ultracold atoms make it possible to create quantum acoustic resonators and explore nonequilibrium dynamics of quantum field theories. These systems offer a promising new platform for studying the dynamical Casimir effect, since they allow to achieve relativistic, i.e. near sonic, velocities of the boundaries. In comparison to previously studied optical and classical hydrodynamic systems ultracold atoms allow to realize a broader class of dynamical experiments combining both classical driving and vacuum squeezing. In this paper we discuss theoretically two types of experiments with interacting one dimensional condensates with moving boundaries. Our analysis is based on the Luttinger liquid model which utilizes the emergent conformal symmetry of the low energy sector of the Lieb-Liniger model. The first system we consider is a variable length interferometer with two Y-junctions connected back to back. We demonstrate that dynamics of the relative phase between the two arms of the interferometer can be analyzed using the formalism developed by Moore in the problem of electromagnetic vacuum squeezing in a cavity with moving mirrors. The second system we discuss is a single condensate in a box potential with periodically moving walls. This system exhibits classical excitation of the mode resonant with the drive as well as nonlinear generation of off-resonant modes. In addition we find strong parametric multimode squeezing between modes whose energy difference matches integer multiples of the drive frequency.

Absence of Luttinger's theorem for fermions with power-law Green functions

We investigate the validity of Luttinger’s theorem (or Luttinger sum rule) in two scale-invariant fermionic models. We find that, in general, Luttinger’s theorem does not hold in a system of fermions with power-law Green functions which do not necessarily preserve particle-hole symmetry. However, Ref. [1,2] showed that Luttinger liquids, another scale-invariant fermionic model, respect Luttinger’s theorem. To understand the difference, we examine the spinless Luttinger liquid model. We find two properties which make the Luttinger sum rule valid in this model: particle-hole symmetry and lmG(\omega=0,-\infty)=0lmG(ω=0,−∞)=0. We conjecture that these two properties represent sufficient, but not necessary, conditions for the validity of the Luttinger sum rule in condensed matter systems.

Out-of-time-ordered correlators in short-range and long-range hard-core boson models and in the Luttinger-liquid model

We study out-of-time-ordered correlators (OTOC) in hard-core boson models with short-range and long-range hopping and compare the results to the OTOC in the Luttinger liquid model. For the density operator, a related `commutator function' starts at zero and decays back to zero after the passage of the wavefront in all three models, while the wavefront broadens as $t^{1/3}$ in the short-range model and shows no broadening in the long-range model and the Luttinger liquid model. For the boson creation operator, the corresponding commutator function shows saturation inside the light cone in all three models, with similar wavefront behavior as in the density-density commutator function, despite the presence of a nonlocal string in terms of Jordan-Wigner fermions. For the long-range model and the Luttinger liquid model, the commutator function decays as power law outside the light cone in the long time regime when following different fixed-velocity rays. In all cases, the OTOCs approach their long-time values in a power-law fashion, with different exponents for different observables and short-range vs long-range cases. Our long-range model appears to capture exponents in the Luttinger liquid model (which are found to be independent of the Luttinger parameter in the model). This conclusion also bears on the OTOC calculations in conformal field theories, which we propose correspond to long-ranged models.

Double light-cone dynamics establish thermal states in integrable 1D Bose gases

We theoretically investigate the non-equilibrium dynamics in a quenched pair of one-dimensional Bose gases with density imbalance. We describe the system using its low-energy effective theory, the Luttinger liquid model. In this framework the system shows strictly integrable relaxation dynamics via dephasing of its approximate many-body eigenstates. In the balanced case, this leads to the well-known light-cone-like establishment of a prethermalized state, which can be described by a generalized Gibbs ensemble. In the imbalanced case the integrable dephasing leads to a state that, counter-intuitively, closely resembles a thermal equilibrium state. The approach to this state is characterized by two separate light-cone dynamics with distinct characteristic velocities. This behavior is a result of the fact that in the imbalanced case observables are not aligned with the conserved quantities of the integrable system. We discuss a concrete experimental realization to study this effect using matterwave interferometry and many-body revivals on an atom chip.

Twofold Torsional Oscillator Experiments from Film to Pressurized Liquid 4He in a Nanometer-Size Channel

We measured the superfluid response of 4He in a one-dimensional channel of 2.8 nm in diameter under unsaturated vapor pressure using a twofold torsional oscillator, and studied whether or not the superfluid response can be explained by the present Tomonaga–Luttinger (TL) liquid model down to the film region. For this system, the superfluid response is accompanied by a large dissipation throughout the film and liquid regions. We observed that the temperature of the dissipation peak is decreased by lowering the measuring frequency from 2 to 0.5 kHz, for a dilute liquid under unsaturated vapor pressure. Furthermore, the decrease becomes small with decreasing density from the pressurized to dilute liquid. On the other hand, no change in the dissipation peak temperature was observed in the film. The results show that, at least down to the liquid under unsaturated vapor pressure, the superfluid response can be explained by the TL liquid model. The dissipation peak itself varies continuously from the thin film t...

Interaction-induced edge states in anisotropic non-Fermi liquids.

We devise an approach to calculation of scaling dimensions of generic operators describing scattering within multi-channel Luttinger liquid. The local impurity scattering in arbitrary configuration of conducting and insulating channels is investigated and the problem is reduced to a single algebraic matrix equation. The application to a semi-infinite array of chains described by Luttinger liquid models demonstrates that for a weak inter-chain hybridisation and intra-channel electron-electron attraction the edge wire is robust against disorder whereas bulk wires, on contrary, become insulating in some region of inter-chain interaction parameters. This result proves that the edge states may exist in disordered anisotropic strongly correlated systems without time-reversal symmetry breaking or spin-orbit interaction and provide quantized low-temperature transport.

Coulomb drag between helical Luttinger liquids

We theoretically study Coulomb drag between two helical edges with broken spin-rotational symmetry, such as would occur in two capacitively coupled quantum spin Hall insulators. For the helical edges, Coulomb drag is particularly interesting because it specifically probes the inelastic interactions that break the conductance quantization for a single edge. Using the kinetic equation formalism, supplemented by bosonization, we find that the drag resistivity $\rho_D$ exhibits a nonmonotonic dependence on the temperature $T$. In the limit of low $T$, $\rho_D$ vanishes with decreasing $T$ as a power law if intraedge interactions are not too strong. This is in stark contrast to Coulomb drag in conventional quantum wires, where $\rho_D$ diverges at $T\to 0$ irrespective of the strength of repulsive interactions. Another unusual property of Coulomb drag between the helical edges concerns higher $T$ for which, unlike in the Luttinger liquid model, drag is mediated by plasmons. The special type of plasmon-mediated drag can be viewed as a distinguishing feature of the helical liquid---because it requires peculiar Umklapp scattering only available in the presence of a Dirac point in the electron spectrum.

Threshold singularities in the correlators of one-dimensional models

We calculate the threshold singularities in one-dimensional models using the universal low-energy formfactors obtained in the framework of the non-linear Luttinger liquid model. We find the reason why a simplified picture of an impurity moving in a Luttinger liquid leads to correct results. We obtain the prefactors of the singularities including their k-dependence at small .