Thermodynamic Bethe Ansatz and Generalised Hydrodynamics in the sine-Gordon model

TL;DR

This paper develops a hydrodynamic framework for non-equilibrium dynamics in the sine-Gordon quantum field theory, utilizing Bethe Ansatz and graphical diagrams to analyze charge and energy transport, including fractal coupling dependence.

Contribution

It introduces a novel hydrodynamic approach based on Bethe Ansatz for the sine-Gordon model, enabling analysis of non-equilibrium phenomena and transport properties.

Findings

Universal fractal dependence of charge Drude weights on coupling

Energy transport quantities lack fractal dependence

Explicit time evolution from bipartite initial states

Abstract

We set up a hydrodynamic description of the non-equilibrium dynamics of sine-Gordon quantum field theory for generic coupling. It is built upon an explicit form of the Bethe Ansatz description of general thermodynamic states, with the structure of the resulting coupled integral equations encoded in terms of graphical diagrams. The resulting framework is applied to derive results for the Drude weights of charge and energy. Quantities associated with the charge universally have fractal dependence on the coupling, which is notably absent from those associated with energy, a feature explained by the different roles played by reflective scattering in transporting these quantities. We then present far-from-equilibrium results, including explicit time evolution starting from bipartite initial states and dynamical correlation functions. Our framework can be applied to explore numerous other aspects of non-equilibrium dynamics, which opens the way to a wide array of theoretical studies and potential novel experimental predictions.