Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium

Abstract

We study the density-density correlation function of the 1D Lieb-Liniger model and obtain an exact expression for the small momentum limit of the static correlator in the thermodynamic limit. We achieve this by summing exactly over the relevant form factors of the density operator in the small momentum limit. The result is valid for any eigenstate, including thermal and non-thermal states. We also show that the small momentum limit of the dynamic structure factors obeys a generalized detailed balance relation valid for any equilibrium state.

32 pages, 4 figures

References in corpus (14)

• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• "Light-cone" dynamics after quantum quenches in spin chains
• Dynamical density-density correlations in the one-dimensional Bose gas
• Generalized Gibbs Ensembles for Quantum Field Theories
• Quantum quench in the sine-Gordon model
• Dynamical structure factor of one-dimensional Bose gases: experimental signatures of beyond-Luttinger liquid physics
• Generalized TBA and generalized Gibbs
• Mean values of local operators in highly excited Bethe states
• Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures
• Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
• Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis
• Density form factors of the 1D Bose gas for finite entropy states
• From the sine-Gordon field theory to the Kardar-Parisi-Zhang growth equation
• Correlation functions of one-dimensional bosons at low temperature

Cited by in corpus (38)

• Entanglement dynamics after quantum quenches in generic integrable systems
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach
• Drude Weight for the Lieb-Liniger Bose Gas
• Correlation functions and transport coefficients in generalised hydrodynamics
• Quench action and Renyi entropies in integrable systems
• Exact large-scale correlations in integrable systems out of equilibrium
• The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
• Generalised hydrodynamics with dephasing noise
• Entanglement spreading in non-equilibrium integrable systems
• Rényi entropies after releasing the Néel state in the XXZ spin-chain
• Exact solution for the quench dynamics of a nested integrable system
• Exact dynamics following an interaction quench in a one-dimensional anyonic gas
• Particle-hole pairs and density-density correlations in the Lieb-Liniger model
• Edge singularities and quasi-long-range order in non-equilibrium steady states
• Thermodynamic bootstrap program for integrable QFT's: Form factors and correlation functions at finite energy density
• Quantum Quench in a Harmonically Trapped One-Dimensional Bose Gas
• A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
• Probing non-thermal density fluctuations in the one-dimensional Bose gas
• Thermalization of interacting quasi-one-dimensional systems
• Quantum Quench in the Infinitely Repulsive Hubbard Model: the Stationary State
• Real-Time Evolution in the Hubbard Model with Infinite Repulsion
• Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
• Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas
• Effective free-fermionic form factors and the XY spin chain
• Analytic thermodynamic properties of the Lieb-Liniger gas
• On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• Correlation properties of a one-dimensional repulsive Bose gas at finite temperature
• Dynamically emergent correlations in bosons via quantum resetting
• The two particle-hole pairs contribution to the dynamic correlation functions of quantum integrable models
• Low-density limit of dynamical correlations in the Lieb-Liniger model
• Rapid filling of the spin gap with temperature in the Schwinger-boson mean-field theory of the antiferromagnetic Heisenberg kagome model
• Mesoscopic density grains in the 1d interacting Bose gas from the exact Yang-Yang solution
• Kubo-Martin-Schwinger relation for an interacting mobile impurity
• Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations
• Cumulants of conserved charges in GGE and cumulants of total transport in GHD: exact summation of matrix elements?
• Full counting statistics after quantum quenches as hydrodynamic fluctuations
• Local Properties of the Rapidity Distribution in the Lieb-Liniger Model