Low temperature dynamics of nonlinear Luttinger liquids

Abstract

We generalize nonlinear Luttinger liquid theory to describe the dynamics of one-dimensional quantum critical systems at low temperatures. Analyzing density-matrix renormalization group results for the spin autocorrelation function in the XXZ chain we provide, in particular, direct evidence for spin diffusion in sharp contrast to the exponential decay in time predicted by conventional Luttinger liquid theory. Furthermore, we discuss how the frequencies and exponents of the oscillatory contributions from the band edges are renormalized by irrelevant interactions and obtain excellent agreement between our finite temperature nonlinear Luttinger liquid theory and the numerical data.

References in corpus (31)

• The density-matrix renormalization group in the age of matrix product states
• Real time evolution using the density matrix renormalization group
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Quantum Quench in the Transverse Field Ising Chain
• The Luttinger model following a sudden interaction switch-on
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Local emergence of thermal correlations in an isolated quantum many-body system
• Universal theory of nonlinear Luttinger liquids
• Far-from-equilibrium spin transport in Heisenberg quantum magnets
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Matrix Product States for dynamical simulation of infinite chains
• Spectral functions in one-dimensional quantum systems at T>0
• Dynamic response of one-dimensional interacting fermions
• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• Probing real-space and time resolved correlation functions with many-body Ramsey interferometry
• Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
• Exact edge singularities and dynamical correlations in spin-1/2 chains
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• Spectral function of spinless fermions on a one-dimensional lattice
• Finite temperature correlations in the Lieb-Liniger 1D Bose gas
• Dynamical structure factor at small q for the XXZ spin-1/2 chain
• Correlations in an expanding gas of hard-core bosons
• Exactly conserved quasilocal operators for the XXZ spin chain
• Fermionic Quasiparticle Representation of Tomonaga-Luttinger Hamiltonian
• Real-time dynamics at finite temperature by DMRG: A path-integral approach
• Energy relaxation and thermalization of hot electrons in quantum wires
• Spin diffusion and the anisotropic spin-1/2 Heisenberg chain
• Spin diffusion in the low-dimensional molecular quantum Heisenberg antiferromagnet Cu(pyz)(NO${}_3$)${}_2$ detected with implanted muons
• Decay of fermionic quasiparticles in one-dimensional quantum liquids
• Femtosecond dynamics of magnetic excitations from resonant inelastic x-ray scattering in CaCu2O3
• Low-energy excitations of a one-dimensional Bose gas with weak contact repulsion

Cited by in corpus (22)

• Finite-temperature transport in one-dimensional quantum lattice models
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Super-diffusion in one-dimensional quantum lattice models
• Superdiffusion from emergent classical solitons in quantum spin chains
• Many-body localization in infinite chains
• Spin-charge separation effects in the low-temperature transport of 1D Fermi gases
• Universal broadening of the light cone in low-temperature transport
• Edge singularities and quasi-long-range order in non-equilibrium steady states
• Exact Quantum Scars in the Chiral Non-Linear Luttinger Liquid
• Equilibrium dynamics of the XX chain
• $T\bar{T}$-deformed conformal field theories out of equilibrium
• Thermal transport in $T\bar{T}$-deformed conformal field theories: from integrability to holography
• Temperature dependence of the NMR spin-lattice relaxation rate for spin-1/2 chains
• Effective free-fermionic form factors and the XY spin chain
• Correlations of zero-entropy critical states in the XXZ model: integrability and Luttinger theory far from the ground state
• Power-law decay of correlations after a global quench in the massive XXZ chain
• The dynamic structure factor in impurity-doped spin chains
• Boundary versus bulk behavior of time-dependent correlation functions in one-dimensional quantum systems
• Open-system spin transport and operator weight dissipation in spin chains
• Dynamical structure factors in the nematic phase of frustrated ferromagnetic spin chains
• From Luttinger liquids to Luttinger droplets via higher-order bosonization identities
• Space-like asymptotics of the thermal two-point functions of the XXZ spin-1/2 chain