Integral equations and large-time asymptotics for finite-temperature Ising chain correlation functions

Abstract

This work concerns the dynamical two-point spin correlation functions of the transverse Ising quantum chain at finite (non-zero) temperature, in the universal region near the quantum critical point. They are correlation functions of twist fields in the massive Majorana fermion quantum field theory. At finite temperature, these are known to satisfy a set of integrable partial differential equations, including the sinh-Gordon equation. We apply the classical inverse scattering method to study them, finding that the ``initial scattering data'' corresponding to the correlation functions are simply related to the one-particle finite-temperature form factors calculated recently by one of the authors. The set of linear integral equations (Gelfand-Levitan-Marchenko equations) associated to the inverse scattering problem then gives, in principle, the two-point functions at all space and time separations, and all temperatures. From them, we evaluate the large-time asymptotic expansion ``near the light cone'', in the region where the difference between the space and time separations is of the order of the correlation length.

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Cited by in corpus (11)

• Exact large-scale correlations in integrable systems out of equilibrium
• Finite Temperature Dynamical Correlations in Massive Integrable Quantum Field Theories
• Particle-hole pairs and density-density correlations in the Lieb-Liniger model
• 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
• Low-Temperature Dynamical Structure Factor of the Two-Leg Spin-1/2 Heisenberg Ladder
• Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
• Form factors in equilibrium and non-equilibrium mixed states of the Ising model
• Correlation functions of twist fields from Ward identities in the massive Dirac theory
• Dynamical correlation functions in the Ising field theory
• Mixed-state form factors of $U(1)$ twist fields in the Dirac theory