Full counting statistics in the sine--Gordon model

TL;DR

This paper provides a comprehensive numerical analysis of full counting statistics in the sine-Gordon model, extending the thermodynamic Bethe Ansatz to compute charge cumulants across all parameters, with comparisons to analytical results.

Contribution

It extends the thermodynamic Bethe Ansatz to the sine-Gordon model for calculating full counting statistics and discusses numerical implementation details.

Findings

Numerical results match analytical predictions in certain limits.

Extended TBA formulation enables full parameter space analysis.

Provides detailed charge cumulant data for the sine-Gordon model.

Abstract

Full counting statistics (FCS) is a dynamical generalisation of the free energy, encapsulating detailed information about the distribution and large-scale correlation functions of conserved charges and their associated currents. In this work, we present a comprehensive numerical study of the FCS and the cumulants of the three lowest charges across the full parameter space of the sine--Gordon field theory. To this end, we extend the thermodynamic Bethe Ansatz (TBA) formulation of the FCS to the sine--Gordon model, emphasise the methodological subtleties for a reliable numerical implementation, and compare numerical results with analytical predictions in certain limits.