Correlation functions and transport coefficients in generalised hydrodynamics

TL;DR

This paper reviews recent exact results on dynamical correlation functions and transport coefficients in interacting integrable models, combining hydrodynamic theory and form-factor methods to understand large-scale behaviors.

Contribution

It synthesizes hydrodynamic and form-factor approaches to provide a comprehensive framework for analyzing transport in integrable systems.

Findings

Explicit expressions for Drude weights and conductivities

Unified description of linear and nonlinear response functions

Applications to spin chains and field theories

Abstract

We review the recent advances on exact results for dynamical correlation functions at large scales and related transport coefficients in interacting integrable models. We discuss Drude weights, conductivity and diffusion constants, as well as linear and nonlinear response on top of equilibrium and non-equilibrium states. We consider the problems from the complementary perspectives of the general hydrodynamic theory of many-body systems, including hydrodynamic projections, and form-factor expansions in integrable models, and show how they provide a comprehensive and consistent set of exact methods to extract large scale behaviours. Finally, we overview various applications in integrable spin chains and field theories.