Luttinger Liquid Research Articles

Ground-state properties of electron-electron biwire systems

The correlation between electrons in different quantum wires is expected to affect the electronic properties of quantum electron-electron biwire systems. Here, we use the variational Monte Carlo method to study the ground-state properties of parallel, infinitely thin electron-electron biwires for several electron densities ($r_\text{s}$) and interwire separations ($d$). Specifically, the ground-state energy, the correlation energy, the interaction energy, the pair-correlation function (PCF), the static structure factor (SSF), and the momentum distribution (MD) function are calculated. We find that the interaction energy increases as $\ln(d)$ for $d\to 0$ and it decreases as $d^{-2}$ when $d\to \infty$. The PCF shows oscillatory behavior at all densities considered here. As two parallel wires approach each other, interwire correlations increase while intrawire correlations decrease as evidenced by the behavior of the PCF, SSF, and MD. The system evolves from two monowires of density parameter $r_\text{s}$ to a single monowire of density parameter $r_\text{s}/2$ as $d$ is reduced from infinity to zero. The MD reveals Tomonaga-Luttinger (TL) liquid behavior with a power-law nature near $k_\text{F}$ even in the presence of an extra interwire interaction between the electrons in biwire systems. It is observed that when $d$ is reduced the MD decreases for $k<k_\text{F}$ and increases for $k>k_\text{F}$, similar to its behavior with increasing $r_\text{s}$. The TL liquid exponent is extracted by fitting the MD data near $k_\text{F}$, from which the TL liquid interaction parameter $K_{\rho}$ is calculated. The value of the TL parameter is found to be in agreement with that of a single wire for large separation between the two wires.

Disorder-enhanced superconductivity in a quasi-one-dimensional strongly correlated system

We perform an analytical and numerical study of a superconducting instability in quasi-one-dimensional (quasi-1D) disordered systems. Modeling them as an array of Luttinger liquids with Josephson-type interchain coupling, we employed renormalization-group analysis with an extensive search for parameters that support superconductivity enhancement. We have found that this phenomenon is possible in the parameters range that support a latent disorder-driven phase transition between charge- and spin-density-wave phases. Our results may explain the experimental observation of disorder-enhanced superconductivity.

Tomonaga-Luttinger Liquid in the Topological Edge Channel of Multilayer FeSe.

A two-dimensional topological insulator exhibits helical edge states topologically protected against single-particle backscattering. Such protection breaks down, however, when electron-electron interactions are significant or when edge reconstruction occurs, leading to a suppressed density of states (DOS) at the Fermi level that follows universal scaling with temperature and energy, characteristic of Tomonaga-Luttinger liquid (TLL). Here, we grow multilayer FeSe on SrTiO3 by molecular beam epitaxy and observe robust edge states at both the {100}Se and the {110}Se steps using scanning tunneling microscopy/spectroscopy. We determine the DOS follows a power law, resulting in the Luttinger parameter K of 0.26 ± 0.02 and 0.43 ± 0.07 for the {100}Se and {110}Se edges, respectively. The smaller K for the {100}Se edge also indicates strong correlations, attributed to ferromagnetic ordering likely present due to checkerboard antiferromagnetic fluctuations in FeSe. These results demonstrate TLL in FeSe helical edge channels, providing an exciting model system for novel topological excitations arising from superconductivity and interacting helical edge states.

Luttinger liquid coupled to Ohmic-class environments

We investigate the impact of an Ohmic-class environment on the conduction and correlation properties of one-dimensional interacting systems. Interestingly, we reveal that inter-particle interactions can be engineered by the environment's noise statistics. Introducing a backscattering impurity to the system, we address Kane-Fisher's metal-to-insulator quantum phase transition in this noisy and realistic setting. Within a perturbative renormalization group approach, we show that the Ohmic environments keep the phase transition intact, while sub- and super-Ohmic environments, modify it into a smooth crossover at a scale that depends on the interaction strength within the wire. The system still undergoes a metal-to-insulator-like transition when moving from sub-Ohmic to super-Ohmic environment noise. We cover a broad range of realistic experimental conditions, by exploring the impact of a finite wire length and temperature on transport through the system.

Enhancement in tunneling density of states in a Luttinger liquid: Role of nonlocal interaction

Power law suppression of local electronic tunneling density of states (TDOS) in the zero-energy limit is a hallmark of Luttinger liquid (LL) phase of the interacting 1-D electron system. We present a theoretical model which hosts LL state with the surprising feature of enhancement rather than suppression in local TDOS originating from non-local and repulsive density-density interactions. Importantly, we find enhancement of TDOS in the manifold of parameter space where the system is stable in the renormalization group (RG) sense. We argue that enhancement of TDOS along with RG stability is possible only when the system has broken parity symmetry about the position of local TDOS enhancement. Such a model could be realized on the edge states of a bi-layer quantum Hall system where both intra-layer and inter-layer density-density interactions are present mimicking the role of local and non-local interactions respectively.

Bosonization study of a generalized statistics model with four Fermi points

We study a one-dimensional lattice model of fractional statistics in which particles have next-nearest-neighbor hopping between sites which depends on the occupation number at the intermediate site and a statistical parameter $\phi$. The model breaks parity and time-reversal symmetries and has four-fermion interactions if $\phi \ne 0$. We first analyze the model using mean field theory and find that there are four Fermi points whose locations depend on $\phi$ and the filling $\eta$. We then study the modes near the Fermi points using the technique of bosonization. Based on the quadratic terms in the bosonized Hamiltonian, we find that the low-energy modes form two decoupled Tomonaga-Luttinger liquids with different values of the Luttinger parameters which depend on $\phi$ and $\eta$; further, the right and left moving modes of each system have different velocities. A study of the scaling dimensions of the cosine terms in the Hamiltonian indicates that the terms appearing in one of the Tomonaga-Luttinger liquids will flow under the renormalization group and the system may reach a non-trivial fixed point in the long distance limit. We examine the scaling dimensions of various charge density and superconducting order parameters to find which of them is the most relevant for different values of $\phi$ and $\eta$. Finally we look at two-particle bound states that appear in this system and discuss their possible relevance to the properties of the system in the thermodynamic limit. Our work shows that the low-energy properties of this model of fractional statistics have a rich structure as a function of $\phi$ and $\eta$.

Ground-state phase diagram of anisotropically interacting Heisenberg- Γ models on a honeycomb lattice

In this paper, we investigate the ground-state phase diagram of the $S=1/2$ Heisenberg-$\mathrm{\ensuremath{\Gamma}}$ model on a honeycomb lattice by dimer series expansion and exact diagonalization. We focus on the effects of the anisotropy of the interactions; by tuning the coupling constants, the system changes between the isolated dimer and the spin-chain models. We find that, in the spin-chain limit, there are three kinds of states: A Tomonaga-Luttinger liquid and two magnetically long-range-ordered states. All three states become two-dimensional long-range-ordered states by the infinitesimal interchain interaction except for the case where the Heisenberg interaction is much weaker than the off-diagonal symmetric $(\mathrm{\ensuremath{\Gamma}})$ interaction. Starting from the isolated dimer limit, a triplet dimer phase survives up to the isotropically interacting system in a large part of the phase diagram where the Heisenberg and $\mathrm{\ensuremath{\Gamma}}$ interactions are ferromagnetic and antiferromagnetic, respectively. Otherwise, a phase transition to a magnetically ordered phase occurs before the interaction becomes isotropic. This indicates that the quantum spin liquid proposed in the $\mathrm{\ensuremath{\Gamma}}$ model [A. Catuneanu et al., npj Quantum Mater. 3, 23 (2018)] is unstable against the anisotropy of the interactions.

Nonequilibrium Floquet Steady States of Time-Periodic Driven Luttinger Liquids

Time-periodic driving facilitates a wealth of novel quantum states and quantum engineering. The interplay of Floquet states and strong interactions is particularly intriguing, which we study using time-periodic fields in a one-dimensional quantum gas, modeled by a Luttinger liquid with periodically changing interactions. By developing a time-periodic operator algebra, we are able to solve and analyze the complete set of nonequilibrium steady states in terms of a Floquet-Bogoliubov ansatz and known analytic functions. Complex valued Floquet eigenenergies occur when integer multiples of the driving frequency approximately match twice the dispersion energy, which correspond to resonant states. In experimental systems of Lieb-Liniger bosons we predict a change from power-law correlations to dominant collective density wave excitations at the corresponding wave numbers as the frequency is lowered below a characteristic cutoff.

Multiple fermion scattering in the weakly coupled spin-chain compound YbAlO3

The Heisenberg antiferromagnetic spin-1/2 chain, originally introduced almost a century ago, is one of the best studied models in quantum mechanics due to its exact solution, but nevertheless it continues to present new discoveries. Its low-energy physics is described by the Tomonaga-Luttinger liquid of spinless fermions, similar to the conduction electrons in one-dimensional metals. In this work we investigate the Heisenberg spin-chain compound YbAlO3 and show that the weak interchain coupling causes Umklapp scattering between the left- and right-moving fermions and stabilizes an incommensurate spin-density wave order at q = 2kF under finite magnetic fields. These Umklapp processes open a route to multiple coherent scattering of fermions, which results in the formation of satellites at integer multiples of the incommensurate fundamental wavevector Q = nq. Our work provides surprising and profound insight into bandstructure control for emergent fermions in quantum materials, and shows how neutron diffraction can be applied to investigate the phenomenon of coherent multiple scattering in metals through the proxy of quantum magnetic systems.

Effective narrow ladder model for two quantum wires on a semiconducting substrate

We present a theoretical study of two spinless fermion wires coupled to a three dimensional semiconducting substrate. We develop a mapping of wires and substrate onto a system of two coupled two-dimensional ladder lattices using a block Lanczos algorithm. We then approximate the resulting system by narrow ladder models, which can be investigated using the density-matrix renormalization group method. In the absence of any direct wire-wire hopping we find that the substrate can mediate an effective wire-wire coupling so that the wires could form an effective two-leg ladder with a Mott charge-density-wave insulating ground state for arbitrarily small nearest-neighbor repulsion. In other cases the wires remain effectively uncoupled even for strong wire-substrate hybridizations leading to the possible stabilization of the Luttinger liquid phase at finite nearest-neighbor repulsion as found previously for single wires on substrates. These investigations show that it may be difficult to determine under which conditions the physics of correlated one-dimensional electrons can be realized in arrays of atomic wires on semiconducting substrates because they seem to depend on the model (and consequently material) particulars.

Two-Fluid Coexistence in a Spinless Fermions Chain with Pair Hopping.

We show that a simple one-dimensional model of spinless fermions with pair hopping displays a phase in which a Luttinger liquid of paired fermions coexists with a Luttinger liquid of unpaired fermions. Our results are based on extensive numerical density-matrix renormalization-group calculations and are supported by a two-fluid model that captures the essence of the coexistence region.

Fractonic topological phases from coupled wires

In three dimensions, gapped phases can support "fractonic" quasiparticle excitations, which are either completely immobile or can only move within a low-dimensional submanifold, a peculiar topological phenomenon going beyond the conventional framework of topological quantum field theory. In this work we explore fractonic topological phases using three-dimensional coupled wire constructions, which have proven to be a successful tool to realize and characterize topological phases in two dimensions. We find that both gapped and gapless phases with fractonic excitations can emerge from the models. In the gapped case, we argue that fractonic excitations are mobile along the wire direction, but their mobility in the transverse plane is generally reduced. We show that the excitations in general have infinite-order fusion structure, distinct from previously known gapped fracton models. Like the 2D coupled wire constructions, many models exhibit gapless (or even chiral) surface states, which can be described by infinite-component Luttinger liquids. However, the universality class of the surface theory strongly depends on the surface orientation, thus revealing a new type of bulk-boundary correspondence unique to fracton phases.

Inelastic Scattering of a Photon by a Quantum Phase Slip.

Spontaneous decay of a single photon is a notoriously inefficient process in nature irrespective of the frequency range. We report that a quantum phase-slip fluctuation in high-impedance superconducting waveguides can split a single incident microwave photon into a large number of lower-energy photons with a near unit probability. The underlying inelastic photon-photon interaction has no analogs in nonlinear optics. Instead, the measured decay rates are explained without adjustable parameters in the framework of a new model of a quantum impurity in a Luttinger liquid. Our result connects circuit quantum electrodynamics to critical phenomena in two-dimensional boundary quantum field theories, important in the physics of strongly correlated systems. The photon lifetime data represent a rare example of verified and useful quantum many-body simulation.

Chiral Anomaly in Interacting Condensed Matter Systems.

The chiral anomaly is a fundamental quantum mechanical phenomenon which is of great importance to both particle physics and condensed matter physics alike. In the context of QED, it manifests as the breaking of chiral symmetry in the presence of electromagnetic fields. It is also known that anomalous chiral symmetry breaking can occur through interactions alone, as is the case for interacting one-dimensional systems. In this Letter, we investigate the interplay between these two modes of anomalous chiral symmetry breaking in the context of interacting Weyl semimetals. Using Fujikawa's path integral method, we show that the chiral charge continuity equation is modified by the presence of interactions which can be viewed as including the effect of the electric and magnetic fields generated by the interacting quantum matter. This can be understood further using dimensional reduction and a Luttinger liquid description of the lowest Landau level. These effects manifest themselves in the nonlinear response of the system. In particular, we find an interaction-dependent density response due to a change in the magnetic field as well as a contribution to the nonequilibrium and inhomogeneous anomalous Hall response while preserving its equilibrium value.

Lifshitz point at commensurate melting of chains of Rydberg atoms

The recent investigation of chains of Rydberg atoms has brought back the problem of commensurate-incommensurate transitions into the focus of current research. In 2D classical systems, or in 1D quantum systems, the commensurate melting of a period-p phase with p larger than 4 is known to take place through an intermediate floating phase where correlations between domain walls or particles decay only as a power law, but when p is equal to 3 or 4, it has been argued by Huse and Fisher that the transition could also be direct and continuous in a non-conformal chiral universality class with a dynamical exponent larger than 1. This is only possible however if the floating phase terminates at a Lifshitz point before reaching the conformal point, a possibility debated since then. Here we argue that this is a generic feature of models where the number of particles is not conserved because the exponent of the floating phase changes along the Pokrovsky-Talapov transition and can thus reach the value at which the floating phase becomes unstable. Furthermore, we show numerically that this scenario is realized in an effective model of the period-3 phase of Rydberg chains in which hard-core bosons are created and annihilated three by three: The Luttinger liquid parameter reaches the critical value $p^2/8=9/8$ along the Pokrovsky-Talapov transition, leading to a Lifshitz point that separates the floating phase from a chiral transition. Implications beyond Rydberg atoms are briefly discussed.

Ground-state phase diagram of the one-dimensional t−Js−Jτ model at quarter filling

We study the ground state of the one-dimensional "$t$-$J_s$-$J_{\tau}$ model," which is a variant of the $t$-$J$ model with additional channel degree of freedom. The model is not only a generalization of the $t$-$J$ model but also an effective model of the two-channel Kondo lattice model in the strong-coupling region. The low-energy excitations and correlation functions are systematically calculated by the density matrix renormalization group method, and the ground-state phase diagram at quarter filling consisting of a Tomonaga-Luttinger liquid, spin-gap state, channel-gap state, insulator, and phase separation is determined. We find that weak channel fluctuations stabilize the spin-gap state, while strong channel fluctuations lead to the transition to the insulator.

Parameters of Tomonaga-Luttinger liquid in a quasi-one-dimensional material with Coulomb interactions

In this work we derive a new scheme to calculate Tomonaga-Luttinger liquid (TLL) parameters and holon (charge modes) velocities in a quasi-1D material that consists of two-leg ladders coupled through Coulomb interactions. Firstly, we obtain an analytic formula for electron-electron interaction potential along the conducting axis for a generalized charge distribution in a plane perpendicular to it. In the second step we introduce many-body screening that is present in a quasi-1D material. To this end we propose a new approximation for the charge susceptibility. Based on this we are able to find the TLL's parameters and velocities. We then show how to use these to validate the experimental ARPES data measured recently in p-polarization in $NbSe_3$. Although we focus our study on this specific material it is applicable for any quasi-1D system that consists of two-leg ladders as basic units.

Fermionic criticality is shaped by Fermi surface topology: a case study of the Tomonaga-Luttinger liquid

We perform a unitary renormalization group (URG) study of the 1D fermionic Hubbard model. The formalism generates a family of effective Hamiltonians and many-body eigenstates arranged holographically across the tensor network from UV to IR. The URG is realized as a quantum circuit, leading to the entanglement holographic mapping (EHM) tensor network description. A topological Θ-term of the projected Hilbert space of the degrees of freedom at the Fermi surface are shown to govern the nature of RG flow towards either the gapless Tomonaga-Luttinger liquid or gapped quantum liquid phases. This results in a nonperturbative version of the Berezenskii-Kosterlitz-Thouless (BKT) RG phase diagram, revealing a line of intermediate coupling stable fixed points, while the nature of RG flow around the critical point is identical to that obtained from the weak-coupling RG analysis. This coincides with a phase transition in the many-particle entanglement, as the entanglement entropy RG flow shows distinct features for the critical and gapped phases depending on the value of the topological Θ-term. We demonstrate the Ryu-Takyanagi entropy bound for the many-body eigenstates comprising the EHM network, concretizing the relation to the holographic duality principle. The scaling of the entropy bound also distinguishes the gapped and gapless phases, implying the generation of very different holographic spacetimes across the critical point. Finally, we treat the Fermi surface as a quantum impurity coupled to the high energy electronic states. A thought-experiment is devised in order to study entanglement entropy generated by isolating the impurity, and propose ways by which to measure it by studying the quantum noise and higher order cumulants of the full counting statistics.

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.

Quench dynamics and relaxation of a spin coupled to interacting leads

We study a quantum quench in which a magnetic impurity is suddenly coupled to Hubbard chains, whose low-energy physics is described by Tomonaga-Luttinger liquid theory. Using the time-dependent density-matrix renormalization-group (tDMRG) technique, we analyze the propagation of charge, spin, and entanglement in the chains after the quench and relate the light-cone velocities to the dispersion of holons and spinons. We find that the local magnetization at the impurity site decays faster if we increase the interaction in the chains, even though the spin velocity decreases. We derive an analytical expression for the relaxation of the impurity magnetization which is in good agreement with the tDMRG results at intermediate timescales, providing valuable insight into the time evolution of the Kondo screening cloud in interacting systems.