Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit

Abstract

We consider zero temperature behavior of dynamic response functions of 1D systems near edges of support in momentum-energy plane $(k,\omega ).$ The description of the singularities of dynamic response functions near an edge $\epsilon (k)$ is given by the effective Hamiltonian of a mobile impurity moving in a Luttinger liquid. For Galilean-invariant systems, we relate the parameters of such an effective Hamiltonian to the properties of the function $\epsilon (k).$ This allows us to express the exponents which characterize singular response functions of spinless bosonic or fermionic liquids in terms of $\epsilon (k)$ and Luttinger liquid parameters for any $k.$ For an antiferromagnetic Heisenberg spin-1/2 chain in a zero magnetic field, SU(2) invariance fixes the exponents from purely phenomenological considerations.

final published version

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Cited by in corpus (38)

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• Spin-charge separation in one-dimensional fermion systems beyond the Luttinger liquid theory
• Magnon damping in the zigzag phase of the Kitaev-Heisenberg-$\Gamma$ model on a honeycomb lattice
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• Dynamical structure factor of one-dimensional hard rods
• Low-energy excitations of a one-dimensional Bose gas with weak contact repulsion
• Relaxation in Luttinger liquids: Bose-Fermi duality
• Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton
• Real-time dynamics in the one-dimensional Hubbard model
• Hierarchy of modes in an interacting system
• Charge and Spin Fractionalization Beyond the Luttinger Liquid Paradigm
• Spin-charge separated quasiparticles in one dimensional quantum fluids
• Variational Bethe Ansatz approach for dipolar one-dimensional bosons
• Exact spectral function of a Tonks-Girardeau gas in a lattice
• One-Dimensional Fermions with neither Luttinger-Liquid nor Fermi-Liquid Behavior
• Spectral edge mode in interacting one-dimensional systems
• Thermal Transport in One Dimensional Electronic Fluid
• Experimental Realization of One Dimensional Helium
• The two particle-hole pairs contribution to the dynamic correlation functions of quantum integrable models
• Equilibration in a chiral Luttinger liquid
• Exact Dynamical Correlations of Hard-Core Anyons in One-Dimensional Lattices
• Exact results of dynamical structure factor of Lieb-Liniger model
• Electron-Plasmon scattering in chiral 1D systems with nonlinear dispersion
• Anomalous Hydrodynamics in One Dimensional Electronic Fluid
• Solitons in a one-dimensional Wigner crystal
• Splitting of Fermi point of strongly interacting electrons in one dimension: A nonlinear effect of spin-charge separation
• Navier-Stokes Equations for Low-Temperature One-Dimensional Fluids
• One-body dynamical correlation function of Lieb-Liniger model at finite temperature
• Spectral function of chiral one-dimensional Fermi liquid in the regime of strong interactions
• Exact spectral function and nonequilibrium dynamics of the strongly interacting Hubbard model
• Universal quasi-Fermi liquid physics of one-dimensional interacting fermions
• Quasi-Fermi liquid behavior in a one-dimensional system of interacting spinless fermions
• Exact Spectral Function of One-Dimensional Bose Gases
• Elementary excitations of a system of one-dimensional chiral fermions with short-range interactions
• Dominant end-tunneling effect in two distinct Luttinger liquids coexisting in one quantum wire