Asymptotics in the bi-Yang-Baxter Sigma Model

Working in a sector of large charge is a powerful tool to analytically access models that are either strongly coupled or otherwise difficult to solve explicitly. In the context of integrable systems, Volin's method is exactly such a large-charge approach. In this note, we apply this method to the bi-Yang-Baxter deformed $SU(2)$ principal chiral model. Our main result is an explicit expression for the free energy density as an asymptotic expansion. We moreover determine the leading non-perturbative effects both via analytic methods and a resurgence analysis.