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 was lacking. In the talk, I will report the filling of this gap by deriving the Thermodynamic Bethe Ansatz framework that captures the thermodynamics of the model and serves as the basis of its hydrodynamic description. As a first application, I will present results on the Drude weight characterising the ballistic transport of the topological charge and demonstrate that its dependence on the value of the coupling features a fractal structure. I will also show recent results about the large-scale fluctuations of the topological charge and current.

 

Based on

https://arxiv.org/abs/2305.10495

https://arxiv.org/abs/2305.15474