Precision estimates of large charge RG exponents $Y_q$ in the 3D XY universality class

Abstract

We accurately compute the RG exponents $Y_q$ of large $q$ fields at the $O(2)$ invariant fixed point in three dimensions. We build on an iterative approach that has been previously proposed and is implemented by using the worm algorithm. We simulate an improved XY model, that has next-to-next-to-nearest couplings in addition to nearest ones. In the worm update we incorporate weights, which allows us to obtain accurate results up to $q=64$. For example we get $Y_q=1.76370(12)$, $0.89167(23)$, and $-0.11203(34)$ for $q=2$, $3$, and $4$, respectively. The comparison with the large $q$ effective field theory gives an excellent agreement down to $q=4$ and provides accurate estimates of the parameters of the effective field theory.