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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>S</a:mi> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>2</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> principal chiral model. Our main result is an explicit expression for the free energy density as an asymptotic expansion. We moreover determine the leading nonperturbative effects both via analytic methods and a resurgence analysis.