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Exact large-scale correlations in integrable systems out of equilibrium

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SciPost Physics

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      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 -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 analyse correlations in the partitioning protocol, extract large-time asymptotics, and, in free models, derive all Euler-scale -point functions.

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        Large Scale Dynamics of Interacting Particles

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          DIFFERENTIAL EQUATIONS FOR QUANTUM CORRELATION FUNCTIONS

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            Author and article information

            Affiliations
            [1 ]King's College London
            Journal
            SciPost Physics
            SciPost Phys.
            Stichting SciPost
            2018
            November 28 2018
            : 5
            : 5
            10.21468/SciPostPhys.5.5.054
            © 2018

            This work is licensed under a Creative Commons Attribution 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

            Physics

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