One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm

Abstract

For many years, the Luttinger liquid theory has served as a useful paradigm for the description of one-dimensional (1D) quantum fluids in the limit of low energies. This theory is based on a linearization of the dispersion relation of the particles constituting the fluid. We review the recent progress in understanding 1D quantum fluids beyond the low-energy limit, where the nonlinearity of the dispersion relation becomes essential. The novel methods which have been developed to tackle such systems combine phenomenology built on the ideas of the Fermi edge singularity and the Fermi liquid theory, perturbation theory in the interaction strength, and a new way of treating finite-size integrable models. These methods can be applied to a wide variety of 1D fluids, from 1D spin liquids to electrons in quantum wires to cold atoms confined to a 1D trap. We review existing results for various dynamic correlation functions, in particular the density structure factor and the spectral function. Moreover, we show how a dispersion nonlinearity leads to finite particle lifetimes, and discuss its impact on the transport properties of 1D systems at finite temperatures. The conventional Luttinger liquid theory is a special limit of the new theory, and we explain the relation between the two.

61 pages, 18 figures, published version, minor typos corrected

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• Spectral Properties of Interacting One-Dimensional Spinless Fermions
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• Spectral functions in a magnetic field as a probe of spin-charge separation in a Luttinger liquid
• Exact spin dynamics of the 1/r^2 supersymmetric t-J model in a magnetic field
• Electron-Plasmon scattering in chiral 1D systems with nonlinear dispersion
• Intersubband Edge Singularity in Metallic Nanotubes
• Density ripples in expanding low-dimensional gases as a probe of correlations
• Non-conformal asymptotic behavior of the time-dependent field-field correlators of 1D anyons
• Dynamical correlation functions of the spin Calogero-Sutherland model
• Large-distance and long-time asymptotic behavior of the reduced density matrix in the non-linear Schrödinger model
• Singular responses of spin-incoherent Luttinger liquids
• RPAE versus RPA for the Tomonaga model with quadratic energy dispersion
• Green's Function of Anyons in Calogero Model and Quantum Hydrodynamics
• On thermal fluctuations in quantum magnets

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• Energy drag in particle-hole symmetric systems as a quantum quench
• Correlations of zero-entropy critical states in the XXZ model: integrability and Luttinger theory far from the ground state
• Dynamical susceptibility of a Fermi liquid
• Magnetic excitations in the one-dimensional Heisenberg-Ising model with external fields and their experimental realizations
• Thermal conductivity of the degenerate one-dimensional Fermi gas
• Necessary and sufficient condition for quantum adiabaticity in a driven one-dimensional impurity-fluid system
• Bosonization for fermions and parafermions
• Spectrum of elementary excitations in Galilean-invariant integrable models
• Bloch oscillations of multi-magnon excitations in a Heisenberg XXZ chain
• Spin-orbital exchange of strongly interacting fermions on the $p$-band of a two-dimensional optical lattice
• Fate of classical solitons in one-dimensional quantum systems
• Universal non-equilibrium states at the fractional quantum Hall edge
• Hot Electrons Regain Coherence in Semiconducting Nanowires
• On singularities of dynamic response functions in the massless regime of the XXZ spin-1/2 chain
• Experimental Realization of One Dimensional Helium
• Polaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity
• Interaction effects in a microscopic quantum wire model with strong spin-orbit interaction
• The two particle-hole pairs contribution to the dynamic correlation functions of quantum integrable models
• Enhanced repulsively bound atom pairs in topological optical lattice ladders
• Interaction-induced backscattering in short quantum wires
• Thermal transport and quench relaxation in nonlinear Luttinger liquids
• Conventional and inverse magnetocaloric and electrocaloric effects of a mixed spin-(1/2, 1) Heisenberg dimer
• Second sound in systems of one-dimensional fermions
• Optical conductivity of the Hubbard chain away from half filling
• Phonon decay in 1D atomic Bose quasicondensates via Beliaev-Landau damping
• Relaxation of phonons in the Lieb-Liniger gas by dynamical refermionization
• Platforms for the realization and characterization of Tomonaga-Luttinger liquids
• The Fine Structure of the Phonon in One Dimension from Quantum Hydrodynamics
• Equilibration in a chiral Luttinger liquid
• Theory of Glide Symmetry Protected Helical Edge States in WTe${}_2$ Monolayer
• Exact results of dynamical structure factor of Lieb-Liniger model
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
• Equilibration of a one-dimensional quantum liquid
• Collective spin modes in Fermi liquids with spin-orbit coupling
• Exact Dynamical Correlations of Hard-Core Anyons in One-Dimensional Lattices
• Hybrid sound modes in one-dimensional quantum liquids
• Dimensional crossover in a Fermi gas from one to effective six dimensions and a cross-dimensional Tomonaga-Luttinger model
• Ground-state energy, density profiles, and momentum distribution of attractively interacting 1D Fermi gases with hard-wall boundaries: a Monte Carlo study
• Luttinger parameter of quasi-one-dimensional para-H2
• Photon echo and fractional excitation lensing of $S=1/2$ XY spin chain
• Mobile impurity approach to the optical conductivity in the Hubbard chain
• Mobile impurity in a one-dimensional gas at finite temperatures
• Evidence for broken Galilean invariance at the quantum spin Hall edge
• Orthogonality catastrophe and fractional exclusion statistics
• Anomalous Hydrodynamics in One Dimensional Electronic Fluid
• One-particle spectral functions of the one-dimensional Fermionic Hubbard model with one fermion per site at zero and finite magnetic fields
• Low-density limit of dynamical correlations in the Lieb-Liniger model
• Pulse propagation in interacting one dimensional Bose liquid
• Entropy production in one-dimensional quantum fluids
• Solitons in a one-dimensional Wigner crystal
• The dynamic structure factor in impurity-doped spin chains
• Few-Body Route to One-Dimensional Quantum Liquids
• Dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field
• Threshold singularities in the correlators of the one-dimensional models
• The fate of quantum shock waves at late times
• Propagation and attenuation of sound in one-dimensional quantum liquids
• Momentum-resolved time evolution with matrix product states
• Landau-Fermi liquids without quasiparticles
• From hardcore Bosons to free Fermions with Painlev{é} V
• Spinon decay in the spin-1/2 Heisenberg chain with weak next nearest neighbour exchange
• Zigzag materials: selective interchain couplings control the coexistence of one-dimensional physics and deviations from it
• Boundary versus bulk behavior of time-dependent correlation functions in one-dimensional quantum systems
• Mobile impurities in integrable models
• Navier-Stokes Equations for Low-Temperature One-Dimensional Fluids
• Hydrodynamics of interacting spinons in the magnetized spin-$1/2$ chain with the uniform Dzyaloshinskii-Moriya interaction
• Structure factor of interacting one-dimensional helical systems
• Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain
• Thermodynamics of one-dimensional SU(4) and SU(6) fermions with attractive interactions
• Splitting of Fermi point of strongly interacting electrons in one dimension: A nonlinear effect of spin-charge separation
• Open-system spin transport and operator weight dissipation in spin chains
• The role of q-spin singlet pairs of physical spins in the dynamical properties of the spin-1/2 Heisenberg-Ising XXZ chain
• Low-Dimensional Fluctuations and Pseudogap in Gaudin-Yang Fermi Gases
• Exact spectral function of the Tonks-Girardeau gas at finite temperature
• Robust one-dimensionality at twin-grain-boundaries in MoSe${}_2$
• Spin-orbit coupling and resonances in the conductance of quantum wires
• A generalized effective spin-chain formalism for strongly interacting spinor gases in optical lattice
• Quantum nonlinear optics on the edge of a few-particle fractional quantum Hall fluid in a small lattice
• Charging a Dimerized Quantum XY Chain
• Spin Seebeck Effect of Triangular-lattice Spin Supersolid
• Quasiparticle decay in a one-dimensional Bose-Fermi mixture
• String orders in the Luttinger liquid phase of one-dimensional spin-1/2 systems
• Integrability breaking and bound states in Google's decorated XXZ circuits
• Emergence of anyonic correlations from spin and charge dynamics in one dimension
• One-dimensional atomic superfluids as a model system for quantum thermodynamics
• Structural Evolution of 1D Spectral Function from Low- to High-Energy Limits
• Correlations in interacting electron liquids: Many-body statistics and hyperuniformity
• Equilibration of Quasi-One-Dimensional Fermi Gases
• Roton in a few-body dipolar system
• Nonlinear Luttinger liquid: Exact result for the Green function in terms of the fourth Painlevé transcendent
• Viscous Properties of a Degenerate One-Dimensional Fermi Gas
• Comment on "Galilean invariance at quantum Hall edge"
• Effects of finite-range interactions on the one-electron spectral properties of one-dimensional metals: Application to Bi/InSb(001)
• Engineering of many-body Majorana states in a topological insulator/s-wave superconductor heterostructure
• Non-thermal Tomonaga-Luttinger liquid eventually emerging from hot electrons in the quantum Hall regime
• Spin incoherent liquid and interaction-driven criticality in 1D Hubbard model
• Measuring the Luttinger liquid parameter with shot noise
• Quantum Many-Body Adiabaticity, Topological Thouless Pump and Driven Impurity in a One-Dimensional Quantum Fluid
• Dynamical structure factors in the nematic phase of frustrated ferromagnetic spin chains
• Orthogonality catastrophe beyond bosonization from post-selection
• Exact ground state and elementary excitations of a competing spin chain with twisted boundary condition
• Local spectral density of an interacting one-dimensional Bose gas with an impurity
• Non-linear edge dynamics of an Integer Quantum Hall fluid
• Observation of spin-charge separation and boundary bound states via the local density of states
• Langevin dynamics of a heavy particle and orthogonality effects
• Plasmon decay and thermal transport from spin-charge coupling in generic Luttinger liquids
• Long time thermal asymptotics of nonlinear Luttinger liquid from inverse scattering
• Thermal radiation as a probe of one-dimensional electron liquids
• One-body dynamical correlation function of Lieb-Liniger model at finite temperature
• Mechanical resonances of mobile impurities in a one-dimensional quantum fluid
• Luttinger parameters of interacting fermions in 1D at high energies
• Viscosity of a Multi-channel One-Dimensional Fermi Gas
• The fate of pairing and spin-charge separation in the presence of long-range antiferromagnetism
• Relaxation of the degenerate one-dimensional Fermi gas
• Effects of finite-range interactions on the one-electron spectral properties of TTF-TCNQ
• Long lifetimes of ultra-hot particles in interacting Fermi systems
• Reply to "Comment on "Galilean invariance at quantum Hall edge""
• Dimensional reduction of the Luttinger-Ward functional for spin-degenerate $D$-dimensional electron gases
• Charge-conserving equilibration of quantum Hall edge states
• Spin correlation functions and quasiparticle decay
• Dispersion relation of a polaron in the Yang-Gaudin Bose gas
• Ground State Properties of Anti-Ferromagnetic Spinor Bose gases in One Dimension
• Spinon and eta-spinon correlation functions
• Dynamical spin structure factor of one-dimensional interacting fermions
• Second-order functional renormalization group approach to quantum wires out of equilibrium
• The weakening of fermionization of one dimensional spinor Bose gases induced by spin-exchange interaction
• Many Body Density of States of a system of non interacting spinless fermions
• Semiconductor nanodevices as a probe of strong electron correlations
• Plasmon localization and relaxation, and thermal transport in one-dimensional conductors
• Phase-space stochastic quantum hydrodynamics for interacting Bose gases
• Microscopic bosonization of band structures: X-ray processes beyond the Fermi edge
• Spin-Triplet Excitonic Insulator in the Ultra-Quantum Limit of HfTe5
• Transport in a One-Dimensional Hyperconductor
• Kinetic processes in Fermi-Luttinger liquids
• Dynamical symmetry and pair tunneling in a one-dimensional Bose gas colliding with a mobile impurity
• Systematic compactification of the two-channel Kondo model. I. Consistent bosonization-debosonization approach and exact comparisons
• Charge fractionalization beyond the Luttinger liquid paradigm: an analytical consideration
• Nonmonotonic plasmon dispersion in strongly interacting Coulomb Luttinger liquids
• Emergent Carroll symmetry at phase separation in one-dimensional lattice systems
• One-dimensional interacting electrons beyond the Dzyaloshinskii-Larkin theorem
• Quasiparticle energy relaxation in a gas of one-dimensional fermions with Coulomb interaction
• Electron-electron interactions in partially mixed helical states
• Bethe strings in the spin dynamical structure factor of the Mott-Hubbard phase in one-dimensional fermionic Hubbard model
• Quantum fluctuating theory for one-dimensional shock waves
• Quantum $z=2$ Lifshitz criticality in one-dimensional interacting fermions
• Finite temperature single-particle Green's function in the Lieb-Liniger model
• Tunneling spectroscopy of the spinon-Kondo effect in one-dimensional Mott insulators
• Refermionized theory of the edge modes of a fractional quantum Hall cloud
• Dissipative Hot-spot Enabled Shock and Bounce Dynamics via Terahertz Quantum Quenches in Helical Edge States
• Threshold singularities in the XXZ- spin chain
• Entanglement entropies of an interval in the free Schrödinger field theory at finite density
• From Luttinger liquids to Luttinger droplets via higher-order bosonization identities
• The interaction energy of the particle-hole pair in the XXZ-spin chain
• Entanglement entropies of an interval in the free Schrödinger field theory on the half line
• Exact Spectral Function of One-Dimensional Bose Gases
• $n$-body Correlation of Tonks-Girardeau Gas
• Caustics in the sine-Gordon model from quenches in coupled 1D Bose gases
• Quasi-Fermi liquid behavior in a one-dimensional system of interacting spinless fermions
• Approaching Periodic Systems in Ensemble Density Functional Theory via Finite One-Dimensional Models
• Space-time first-order correlations of an open Bose-Hubbard model with incoherent pump and loss
• Universal quasi-Fermi liquid physics of one-dimensional interacting fermions
• Nonlinear effects on charge fractionalization in critical chains
• Perfect Wave Transfer in Continuous Quantum Systems
• Universal thermalization dynamics in (1+1)d QFTs
• Spin Seebeck effect of interacting spinons
• Particle Propagator of Spin Calogero-Sutherland Model
• Dynamic structure factor of Calogero-Sutherland fluids
• Nonequilibrium plasmon liquid in a Josephson junction chain
• Quantum Transport Protected by Acceleration From Nonadiabaticity and Dissipation
• Sliding phasons in Moiré Ladders
• Ising spin-1/2 XXZ chain's quantum problems beyond the spinon paradigm
• Nonlinear edge transport in a quantum Hall system
• Robust Luttinger liquid state of 1D Dirac fermions in a van der Waals system Nb${}_9$Si${}_4$Te${}_{18}$
• Universality in Non-Equilibrium Quantum Systems
• Brownian scattering of a spinon in a Luttinger liquid
• Decay of the Kohn mode in hydrodynamic regime
• Quantum Monte Carlo study of strongly interacting bosonic one-dimensional systems in periodic potentials
• Elementary excitations of a system of one-dimensional chiral fermions with short-range interactions
• Magnetic excitations and exchange parameters of a nickel chain compound PbMn${}_2$Ni${}_6$Te${}_3$O${}_{18}$: Neutron scattering and density functional theory studies
• Controlling correlations of a polaritonic Luttinger liquid by engineered cross-Kerr nonlinearity
• Thermal liquid-gas phase transition in a quasi-one-dimensional dipolar Fermi gas
• Emergent electronic insulating states in a one-dimensional moiré superlattice
• Electronic correlations in magnetized helical edge states coupled to s-wave superconductors
• Local Properties of the Rapidity Distribution in the Lieb-Liniger Model
• Emergent dipole field theory in atomic ladders
• Exact results, transient generalized Gibbs ensembles, and analytic approximations for spacetime propagators of massive, real scalar fields in one spatial dimension
• Functional Renormalization Group for fermions on a one dimensional lattice at arbitrary filling
• One-dimensional extended Hubbard model with soft-core potential
• Thermalization of dipole oscillations in confined systems by rare collisions
• Quantum wake dynamics in Heisenberg antiferromagnetic chains
• Quench Dynamics of Anyon Tonks-Girardeau Gases
• Non-integrable fermionic chains near criticality
• Investigating the roots of the nonlinear Luttinger liquid phenomenology
• Hole-induced anomaly in the thermodynamic behavior of a one-dimensional Bose gas
• Momentum Evolution Numerics of an Impurity in a Quantum Quench
• One-particle spectral function singularities in a one-dimensional gas of spin-1/2 fermions with repulsive delta-function interaction