Exact large-scale correlations in integrable systems out of equilibrium

TL;DR

This paper derives exact Euler-scale two-point correlation functions in inhomogeneous, non-stationary states of integrable systems using generalized hydrodynamics, extending previous results to more general settings and providing a recursive method for n-point functions.

Contribution

It introduces a new recursive technique for calculating n-point correlation functions in integrable systems, applicable to both quantum and classical models, including inhomogeneous and non-stationary states.

Findings

Derived exact two-point functions for conserved densities and currents.

Established formulae for arbitrary local fields from homogeneous one-point functions.

Applied results to models like sinh-Gordon, Lieb-Liniger, XXZ, and Hubbard.

Abstract

Using the theory of generalized hydrodynamics (GHD), we derive exact Euler-scale dynamical two-point correlation functions of conserved densities and currents in inhomogeneous, non-stationary states of many-body integrable systems with weak space-time variations. This extends previous works to inhomogeneous and non-stationary situations. Using GHD projection operators, we further derive formulae for Euler-scale two-point functions of arbitrary local fields, purely from the data of their homogeneous one-point functions. These are new also in homogeneous generalized Gibbs ensembles. The technique is based on combining a fluctuation-dissipation principle along with the exact solution by characteristics of GHD, and gives a recursive procedure able to generate $n$-point correlation functions. Owing to the universality of GHD, the results are expected to apply to quantum and classical integrable field theory such as the sinh-Gordon model and the Lieb-Liniger model, spin chains such as the XXZ and Hubbard models, and solvable classical gases such as the hard rod gas and soliton gases. In particular, we find Leclair-Mussardo-type infinite form-factor series in integrable quantum field theory, and exact Euler-scale two-point functions of exponential fields in the sinh-Gordon model and of powers of the density field in the Lieb-Liniger model. We also analyze correlations in the partitioning protocol, extract large-time asymptotics, and, in free models, derive all Euler-scale $n$-point functions.