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 nn-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 nn-point functions.

Highlights

  • 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

  • The results are expressed solely in terms of quantities that are available within the thermodynamic Bethe ansatz framework

  • They are valid at the Euler scale, where variations of averages of local fields occur on very large scales

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Summary

Introduction

The nonequilibrium dynamics of integrable many-body systems has received a large amount of attention recently, especially in view of experimental realizations in cold atomic gases [1,2,3]. Using the BertiniPiroli-Calabrese simplification of the Negro-Smirnov formula [50,51,52] we obtain explicit results for two-point functions of exponential fields in the sinh-Gordon model, and using Pozsgay’s formula [81], of powers of the density operator in the Lieb-Liniger model These constitute the first such exact results in inhomogeneous, non-stationary states, and in homogeneous GGEs. we obtain all Euler-scale n-point functions in free models, study two-point functions of conserved densities in the partitioning protocol, obtaining a number of new results for its solution by characteristics, and study the large-time asymptotics of two-point functions from arbitrary inhomogeneous initial conditions.

Review of GHD
GGEs in the quasi-particle formulation
Generalized fluids in space-time
Time evolution
Correlation functions
Generating higher-point correlation functions
Exact two-point functions of densities and currents
Connection with hydrodynamic projections
Re-writing in hydrodynamic-projection form
Examples
Discussion and analysis
Conclusion
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