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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• Thirty Years of Composite Fermions and Beyond
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• Strongly interacting trapped one-dimensional quantum gases: an exact solution
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• Prethermalization and Thermalization of a Quenched Interacting Luttinger Liquid
• Third-order perturbative lattice and complex Langevin analyses of the finite-temperature equation of state of non-relativistic fermions in one dimension
• Taming electronic decoherence in 1D chiral ballistic quantum conductors
• Exponential Orthogonality Catastrophe in Single-Particle and Many-Body Localized Systems
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• Equilibration in a chiral Luttinger liquid
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• From Luttinger liquids to Luttinger droplets via higher-order bosonization identities
• Perfect Wave Transfer in Continuous Quantum Systems
• Universal thermalization dynamics in (1+1)d QFTs
• The interaction energy of the particle-hole pair in the XXZ-spin chain
• $n$-body Correlation of Tonks-Girardeau Gas
• Caustics in the sine-Gordon model from quenches in coupled 1D Bose gases
• Quantum Transport Protected by Acceleration From Nonadiabaticity and Dissipation
• Nonequilibrium plasmon liquid in a Josephson junction chain
• Brownian scattering of a spinon in a Luttinger liquid
• Spin Seebeck effect of interacting spinons
• Space-time first-order correlations of an open Bose-Hubbard model with incoherent pump and loss
• Universality in Non-Equilibrium Quantum Systems
• Universal quasi-Fermi liquid physics of one-dimensional interacting fermions
• Local Properties of the Rapidity Distribution in the Lieb-Liniger Model
• One-particle spectral function singularities in a one-dimensional gas of spin-1/2 fermions with repulsive delta-function interaction
• Controlling correlations of a polaritonic Luttinger liquid by engineered cross-Kerr nonlinearity
• Quantum wake dynamics in Heisenberg antiferromagnetic chains
• 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
• Momentum Evolution Numerics of an Impurity in a Quantum Quench
• Emergent electronic insulating states in a one-dimensional moiré superlattice
• Thermalization of dipole oscillations in confined systems by rare collisions
• Non-integrable fermionic chains near criticality
• Quench Dynamics of Anyon Tonks-Girardeau Gases
• Investigating the roots of the nonlinear Luttinger liquid phenomenology
• Hole-induced anomaly in the thermodynamic behavior of a one-dimensional Bose gas
• Quantum Monte Carlo study of strongly interacting bosonic one-dimensional systems in periodic potentials
• Exact results, transient generalized Gibbs ensembles, and analytic approximations for spacetime propagators of massive, real scalar fields in one spatial dimension
• Emergent dipole field theory in atomic ladders
• Functional Renormalization Group for fermions on a one dimensional lattice at arbitrary filling
• Electronic correlations in magnetized helical edge states coupled to s-wave superconductors
• One-dimensional extended Hubbard model with soft-core potential
• Thermal liquid-gas phase transition in a quasi-one-dimensional dipolar Fermi gas