Full counting statistics in the sine--Gordon model

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.