Long time correlations of nonlinear Luttinger liquids

Abstract

An overview is given of the limitations of Luttinger liquid theory in describing the real time equilibrium dynamics of critical one-dimensional systems with nonlinear dispersion relation. After exposing the singularities of perturbation theory in band curvature effects that break the Lorentz invariance of the Tomonaga-Luttinger model, the origin of high frequency oscillations in the long time behaviour of correlation functions is discussed. The notion that correlations decay exponentially at finite temperature is challenged by the effects of diffusion in the density-density correlation due to umklapp scattering in lattice models.

17 pages, 3 figures. Short review to appear in the Luttinger Liquids special issue of Int. J. Mod. Phys. B; reference added

References in corpus (17)

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Cited by in corpus (17)

• Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution
• Exact real-time longitudinal correlation functions of the massive XXZ chain
• A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
• Real-time dynamics in the one-dimensional Hubbard model
• Periodic Airy process and equilibrium dynamics of edge fermions in a trap
• Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet
• Spin-charge separated quasiparticles in one dimensional quantum fluids
• Correlations of zero-entropy critical states in the XXZ model: integrability and Luttinger theory far from the ground state
• Low-density limit of dynamical correlations in the Lieb-Liniger model
• Mobile impurity approach to the optical conductivity in the Hubbard chain
• Boundary versus bulk behavior of time-dependent correlation functions in one-dimensional quantum systems
• Dynamical structure factors in the nematic phase of frustrated ferromagnetic spin chains
• Detecting Spin Transport in Quantum Magnets with Photons
• Numerical study of the temperature dependence of the NMR relaxation rate across the superfluid-Bose glass transition in one dimension
• Nonlinear effects on charge fractionalization in critical chains
• Quasi-Fermi liquid behavior in a one-dimensional system of interacting spinless fermions
• Universal quasi-Fermi liquid physics of one-dimensional interacting fermions