Form factor expansion for thermal correlators

Abstract

We consider finite temperature correlation functions in massive integrable Quantum Field Theory. Using a regularization by putting the system in finite volume, we develop a novel approach (based on multi-dimensional residues) to the form factor expansion for thermal correlators. The first few terms are obtained explicitly in theories with diagonal scattering. We also discuss the validity of the LeClair-Mussardo proposal.

41 pages; v2: minor corrections, v3: minor corrections

References in corpus (36)

• Exciting Collective Oscillations in a Trapped 1D Gas
• Yang-Yang thermodynamics on an atom chip
• Non-integrable Quantum Field Theories as Perturbations of Certain Integrable Models
• Dynamical density-density correlations in the one-dimensional Bose gas
• Integral representations for correlation functions of the XXZ chain at finite temperature
• Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field
• Algebraic Aspects of Bethe-Ansatz
• Finite Temperature Correlation Functions in Integrable QFT
• Form factors in finite volume II:disconnected terms and finite temperature correlators
• Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime
• Asymptotic factorisation of form factors in two-dimensional quantum field theory
• Form factors in finite volume I: form factor bootstrap and truncated conformal space
• Expectation Values in the Lieb-Liniger Bose Gas
• Finite-temperature lineshapes in gapped quantum spin chains
• A comment on finite temperature correlations in integrable QFT
• Finite temperature correlations in the one-dimensional quantum Ising model
• Integrability of quantum chains: theory and applications to the spin-1/2 $XXZ$ chain
• Haldane Gapped Spin Chains: Exact Low Temperature Expansions of Correlation Functions
• Low temperature correlation functions in integrable models: Derivation of the large distance and time asymptotics from the form factor expansion
• Correlation Functions in the Two-dimensional Ising Model in a Magnetic Field at $T=T_c$
• Finite temperature expectation values of local fields in the sinh-Gordon model
• One-point functions in massive integrable QFT with boundaries
• Finite temperature correlation functions from form factors
• A note on the spin-1/2 XXZ chain concerning its relation to the Bose gas
• The form factors in the finite volume
• On the Finite Temperature Formalism in Integrable Quantum Field Theories
• Finite-Volume Form Factors in Semiclassical Approximation
• Form factor perturbation theory from finite volume
• Boundary form factors in finite volume
• One-point functions in integrable quantum field theory at finite temperature
• Bethe Ansatz Matrix Elements as Non-Relativistic Limits of Form Factors of Quantum Field Theory
• The determinant representation for quantum correlation functions of the sinh-Gordon model
• On the space of quantum fields in massive two-dimensional theories
• Finite temperature expectation values of boundary operators
• The Determinant Representation for a Correlation Function in Scaling Lee-Yang Model
• Two-point correlation functions in perturbed minimal models

Cited by in corpus (51)

• Quantum Quench in the Transverse Field Ising Chain
• Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Quantum quench in the sine-Gordon model
• Dynamics in the Ising field theory after a quantum quench
• Correlation functions and transport coefficients in generalised hydrodynamics
• Exact large-scale correlations in integrable systems out of equilibrium
• Mean values of local operators in highly excited Bethe states
• Boundary State in an Integrable Quantum Field Theory Out of Equilibrium
• Structure constants at wrapping order
• How order melts after quantum quenches
• Particle-hole pairs and density-density correlations in the Lieb-Liniger model
• Density form factors of the 1D Bose gas for finite entropy states
• Overlap singularity and time evolution in integrable quantum field theory
• Finite temperature spin dynamics in a perturbed quantum critical Ising chain with an $E_8$ symmetry
• Thermodynamic Bethe ansatz for non-equilibrium steady states: exact energy current and fluctuations in integrable QFT
• 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
• A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
• On Form Factors in nested Bethe Ansatz systems
• Hexagons and Correlators in the Fishnet Theory
• Spectral expansion for finite temperature two-point functions and clustering
• Thermalization of interacting quasi-one-dimensional systems
• Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
• Diagonal multi-soliton matrix elements in finite volume
• LeClair-Mussardo series for two-point functions in Integrable QFT
• Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas
• Sine-Gordon multi-soliton form factors in finite volume
• Finite temperature dynamics in gapped 1D models in the sine-Gordon family
• Effective free-fermionic form factors and the XY spin chain
• Exact finite volume expectation values of local operators in excited states
• On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• Finite temperature one-point functions in non-diagonal integrable field theories: the sine-Gordon model
• Divergent nonlinear response from quasiparticle interactions
• Local dynamics and thermal activation in the transverse-field Ising chain
• Field theoretical derivation of Lüscher's formula and calculation of finite volume form factors
• Inelastic decay from integrability
• The two particle-hole pairs contribution to the dynamic correlation functions of quantum integrable models
• Regularization of multi-soliton form factors in sine-Gordon model
• Radiative corrections to the quark masses in the ferromagnetic Ising and Potts field theories
• Decay of long-lived oscillations after quantum quenches in gapped interacting quantum systems
• Nontrivial Thermodynamics in 't Hooft's Large-$N$ Limit
• Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations
• Sine-Gordon model at finite temperature: the method of random surfaces
• Entanglement Entropy in Integrable Field Theories with Line Defects I. Topological Defect
• Entanglement of Stationary States in the Presence of Unstable Quasiparticles
• Thermally activated detection of dark particles in a weakly coupled quantum Ising ladder
• Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems
• Mixed-state form factors of $U(1)$ twist fields in the Dirac theory
• Confinement-Higgs Phase Crossover as a Lattice Artifact in 1+1 Dimensions
• Dynamical correlation functions in the Ising field theory