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

TL;DR

This paper accurately computes large charge RG exponents in the 3D XY universality class using an improved model and worm algorithm, achieving high precision for a range of q values and validating effective field theory predictions.

Contribution

It introduces an enhanced iterative approach with worm algorithm simulations to precisely estimate RG exponents for large charges in the 3D XY model.

Findings

Accurate RG exponents for q up to 64.

Excellent agreement with effective field theory for q ≥ 4.

Precise parameter estimates for the effective field theory.

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.