Thermodynamics and fractal Drude weights in the sine-Gordon model

The sine-Gordon model is a paradigmatic quantum field theory that provides the low-energy effective description of many gapped 1D systems. Despite this fact, its complete thermodynamic description in all its regimes has been lacking. Here we fill this gap and derive the framework that captures its thermodynamics and serves as the basis of its hydrodynamic description. As a first application, we compute the Drude weight characterising the ballistic transport of topological charge and demonstrate that its dependence on the value of the coupling shows a fractal structure, similar to the gapless phase of the XXZ spin chain. The thermodynamic framework can be applied to study other features of non-equilibrium dynamics in the sine-Gordon model using generalised hydrodynamics, opening the way to a wide array of theoretical studies and potential novel experimental predictions.