The two particle-hole pairs contribution to the dynamic correlation functions of quantum integrable models

Abstract

We consider the problem of computing dynamic correlation functions of quantum integrable models employing the thermodynamic form-factor approach. Specifically, we focus on correlations of local operators that conserve the number of particles and consider the 2-particle-hole contribution to their two-point functions. With the method developed being generally applicable to any finite energy and entropy state, our primary focus is on the thermal states. To exemplify this approach, we chose the Lieb-Liniger model and study the leading contribution from 2-particle-hole excitations at small momenta to the dynamic density-density correlation function. We also consider analogous contributions to two-point functions of higher local conserved densities and currents present in integrable theories.

arXiv comment27 pages, 1 figure, revised version

References in corpus (69)

• Thermalization and its mechanism for generic isolated quantum systems
• Nonequilibrium dynamics of closed interacting quantum systems
• Quantum many-body systems out of equilibrium
• Time-dependence of correlation functions following a quantum quench
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• 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
• Generalized HydroDynamics on an Atom Chip
• Hydrodynamic Diffusion in Integrable Systems
• Ultracold atoms out of equilibrium
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Soliton gases and generalized hydrodynamics
• Constructing the generalized Gibbs ensemble after a quantum quench
• Universal theory of nonlinear Luttinger liquids
• Solvable Hydrodynamics of Quantum Integrable Systems
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Large-scale description of interacting one-dimensional Bose gases: generalized hydrodynamics supersedes conventional hydrodynamics
• The Quench Action
• Quantum Quenches in Integrable Field Theories
• Dynamical density-density correlations in the one-dimensional Bose gas
• 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
• Quantum quench in the sine-Gordon model
• One-particle dynamical correlations in the one-dimensional Bose gas
• Dynamical structure factor of one-dimensional Bose gases: experimental signatures of beyond-Luttinger liquid physics
• Generalized hydrodynamics with space-time inhomogeneous interactions
• Generalized TBA and generalized Gibbs
• Exact local correlations and full counting statistics for arbitrary states of the one-dimensional interacting Bose gas
• Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
• Exact exponents of edge singularities in dynamic correlation functions of 1D Bose gas
• Finite temperature correlations in the Lieb-Liniger 1D Bose gas
• Determinant representation for dynamical correlation functions of the Quantum nonlinear Schrödinger equation
• Exact large-scale correlations in integrable systems out of equilibrium
• 1D Lieb-Liniger Bose Gas as Non-Relativistic Limit of the Sinh-Gordon Model
• Generalized hydrodynamics of classical integrable field theory: the sinh-Gordon model
• Momentum transferred to a trapped Bose-Einstein condensate by stimulated light scattering
• Form factor expansion for thermal correlators
• Correlation Functions of the Quantum Sine-Gordon Model in and out of Equilibrium
• Exact prefactors in static and dynamic correlation functions of 1D quantum integrable models: applications to the Calogero-Sutherland, Lieb-Liniger and XXZ models
• Momentum-resolved study of an array of 1D strongly phase-fluctuating Bose gases
• Nonuniversal prefactors in correlation functions of 1D quantum liquids
• On one-point functions for sinh-Gordon model at finite temperature
• Finite-temperature form factors in the free Majorana theory
• Finite Temperature Dynamical Correlations in Massive Integrable Quantum Field Theories
• Thermal form-factor approach to dynamical correlation functions of integrable lattice models
• From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics
• Finite temperature correlation functions from form factors
• Generalized hydrodynamics regime from the thermodynamic bootstrap program
• 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
• Finite-Temperature Form Factors: a Review
• Density form factors of the 1D Bose gas for finite entropy states
• 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
• Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions
• Dynamic and static density-density correlations in the one-dimensional Bose gas: exact results and approximations
• Measuring effective temperatures in a generalized Gibbs ensemble
• A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
• Quantum quench in the attractive regime of the sine-Gordon model
• Probing non-thermal density fluctuations in the one-dimensional Bose gas
• The Cauchy Principal Value and the finite part integral as values of absolutely convergent integrals
• Microscopic approach to a class of 1D quantum critical models
• Bethe Ansatz Matrix Elements as Non-Relativistic Limits of Form Factors of Quantum Field Theory
• Linearized regime of the generalized hydrodynamics with diffusion
• High-temperature analysis of the transverse dynamical two-point correlation function of the XX quantum-spin chain
• Hydrodynamics of local excitations after an interaction quench in 1D cold atomic gases
• Late-time large-distance asymptotics of the transverse correlation functions of the XX chain in the space-like regime

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• Correlation functions and transport coefficients in generalised hydrodynamics
• Diffusive Hydrodynamics of Inhomogenous Hamiltonians
• Thermalization of interacting quasi-one-dimensional systems
• 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
• On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• Navier-Stokes equations for nearly integrable quantum gases
• Prethermalization in coupled one-dimensional quantum gases
• Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations
• Extending the Thermodynamic Form Factor Bootstrap Program: Multiple particle-hole excitations, crossing symmetry, and reparameterization invariance