A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model

Abstract

We introduce a framework for calculating dynamical correlations in the Lieb-Liniger model in arbitrary energy eigenstates and for all space and time, that combines a Lehmann representation with a $1/c$ expansion. The $n^{\mathrm{th}}$ term of the expansion is of order $1/c^n$ and takes into account all $\lfloor \frac{n}{2}\rfloor +1$ particle-hole excitations over the averaging eigenstate. Importantly, in contrast to a 'bare' $1/c$ expansion it is uniform in space and time. The framework is based on a method for taking the thermodynamic limit of sums of form factors that exhibit non integrable singularities. We expect our framework to be applicable to any local operator. We determine the first three terms of this expansion and obtain an explicit expression for the density-density dynamical correlations and the dynamical structure factor at order $1/c^2$. We apply these to finite-temperature equilibrium states and non-equilibrium steady states after quantum quenches. We recover predictions of (nonlinear) Luttinger liquid theory and generalized hydrodynamics in the appropriate limits, and are able to compute sub-leading corrections to these.

arXiv comment78 pages; corresponds to published version

References in corpus (79)

• Nonequilibrium dynamics of closed interacting quantum systems
• Light-cone-like spreading of correlations in a quantum many-body system
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Generalized Gibbs ensemble in integrable lattice models
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Time evolution of local observables after quenching to an integrable model
• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Bosonizing one-dimensional cold atomic gases
• Quantum quenches in 1+1 dimensional conformal field theories
• Generalized Thermalization in an Integrable Lattice System
• Solution for an interaction quench in the Lieb-Liniger Bose gas
• Solvable Hydrodynamics of Quantum Integrable Systems
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Microscopic origin of ideal conductivity in integrable quantum models
• The Quench Action
• Dynamical density-density correlations in the one-dimensional Bose gas
• Dynamical Correlations after a Quantum Quench
• Probing the Excitations of a Lieb-Liniger Gas from Weak to Strong Coupling
• Finite Temperature Correlation Functions in Integrable QFT
• Drude Weight for the Lieb-Liniger Bose Gas
• One-particle dynamical correlations in the one-dimensional Bose gas
• Form factor approach to dynamical correlation functions in critical models
• Dynamical structure factor of one-dimensional Bose gases: experimental signatures of beyond-Luttinger liquid physics
• Interaction quenches in the 1D Bose gas
• Temperature Correlations of Quantum Spins
• Spectral function of spinless fermions on a one-dimensional lattice
• Exact exponents of edge singularities in dynamic correlation functions of 1D Bose gas
• Multi-particle bound state formation following a quantum quench to the one-dimensional Bose gas with attractive interactions
• Finite temperature correlations in the Lieb-Liniger 1D Bose gas
• Exact large-scale correlations in integrable systems out of equilibrium
• 1D Lieb-Liniger Bose Gas as Non-Relativistic Limit of the Sinh-Gordon Model
• Finite-temperature lineshapes in gapped quantum spin chains
• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• A comment on finite temperature correlations in integrable QFT
• Form factor expansion for thermal correlators
• Finite temperature correlations in the one-dimensional quantum Ising model
• Universal correlations of trapped one-dimensional impenetrable bosons
• New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain
• Exact prefactors in static and dynamic correlation functions of 1D quantum integrable models: applications to the Calogero-Sutherland, Lieb-Liniger and XXZ models
• Haldane Gapped Spin Chains: Exact Low Temperature Expansions of Correlation Functions
• Nonuniversal prefactors in correlation functions of 1D quantum liquids
• Low temperature correlation functions in integrable models: Derivation of the large distance and time asymptotics from the form factor expansion
• Finite-temperature form factors in the free Majorana theory
• Density matrices for finite segments of Heisenberg chains of arbitrary length
• Finite Temperature Dynamical Correlations in Massive Integrable Quantum Field Theories
• Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
• Relaxation dynamics of local observables in integrable systems
• How order melts after quantum quenches
• Thermal form-factor approach to dynamical correlation functions of integrable lattice models
• Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain
• Thermal form factors of the XXZ chain and the large-distance asymptotics of its temperature dependent correlation functions
• Momentum-space correlations of a one-dimensional Bose gas
• Short-distance thermal correlations in the massive XXZ chain
• Generalized hydrodynamics regime from the thermodynamic bootstrap program
• The Dynamic Structure Factor of the 1D Bose Gas near the Tonks-Girardeau Limit
• Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium
• Particle-hole pairs and density-density correlations in the Lieb-Liniger model
• Low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain
• Density form factors of the 1D Bose gas for finite entropy states
• On the thermodynamic limit of form factor expansions of dynamical correlation functions in the massless regime of the XXZ spin $1/2$ chain
• Thermodynamic bootstrap program for integrable QFT's: Form factors and correlation functions at finite energy density
• Short-distance thermal correlations in the XXZ chain
• Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions
• Finite Temperature Dynamical Structure Factor of the Heisenberg-Ising Chain
• Dynamic and static density-density correlations in the one-dimensional Bose gas: exact results and approximations
• Equilibrium dynamics of the XX chain
• The form factors in the finite volume
• Quantum Projectors and Local Operators in Lattice Integrable Models
• NMR relaxation in Ising spin chains
• Microscopic approach to a class of 1D quantum critical models
• Finite temperature correlation function for one-dimensional Quantum Ising model: the virial expansion
• Long time correlations of nonlinear Luttinger liquids
• High-temperature analysis of the transverse dynamical two-point correlation function of the XX quantum-spin chain
• On Form Factors of the conjugated field in the non-linear Schröodinger model
• Late-time large-distance asymptotics of the transverse correlation functions of the XX chain in the space-like regime
• Integral equations and large-time asymptotics for finite-temperature Ising chain correlation functions
• Nonlinear Luttinger liquid: Exact result for the Green function in terms of the fourth Painlevé transcendent

Cited by in corpus (29)

• Superdiffusion in spin chains
• Correlation functions and transport coefficients in generalised hydrodynamics
• Non-Equilibrium Dynamics and Weakly Broken Integrability
• Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
• Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54
• A short introduction to Generalized Hydrodynamics
• Form factors and generalized hydrodynamics for integrable systems
• Hydrodynamic gauge fixing and higher order hydrodynamic expansion
• Field-theoretical aspects of one-dimensional Bose and Fermi gases with contact interactions
• Diffusive Hydrodynamics of Inhomogenous Hamiltonians
• 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
• Systematic strong coupling expansion for out-of-equilibrium dynamics in the Lieb-Liniger model
• BBGKY Hierarchy and Generalised Hydrodynamics
• On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• An integrable spin chain with Hilbert space fragmentation and solvable real time dynamics
• The two particle-hole pairs contribution to the dynamic correlation functions of quantum integrable models
• Exact results of dynamical structure factor of Lieb-Liniger model
• Low-density limit of dynamical correlations in the Lieb-Liniger model
• Duality between weak and strong interactions in quantum gases
• Exact spectral function of the Tonks-Girardeau gas at finite temperature
• The relevant excitations for the one-body function in the Lieb-Liniger model
• One-body dynamical correlation function of Lieb-Liniger model at finite temperature
• Regularization of a strong-weak duality between pointlike interactions in one dimension
• Interaction induced Anderson transition in a kicked one dimensional Bose gas
• Wavelet representation of hardcore bosons
• Finite temperature single-particle Green's function in the Lieb-Liniger model
• Hole-induced anomaly in the thermodynamic behavior of a one-dimensional Bose gas