Large-charge conformal dimensions at the $O(N)$ Wilson-Fisher fixed point

Abstract

Recent work using a large-charge expansion for the $O(N)$ Wilson-Fisher conformal field theory has shown that the anomalous dimensions of large-charge operators can be expressed in terms of a few low-energy constants (LECs) of a large-charge effective field theory (EFT). By performing lattice Monte Carlo computations at the $O(N)$ Wilson-Fisher fixed point, we compute the anomalous dimensions of large-charge operators up to $N=8$ and charge $Q=10$, and extract the leading and subleading LECs of the $O(N)$ large-charge EFT. To alleviate the signal-to-noise ratio problem present in the large-charge sector of conventional lattice formulations of the $O(N)$ theory, we employ a recently developed qubit formulation of the $O(N)$ nonlinear sigma models with a worm algorithm. This enables us to test the validity of the large-charge expansion and the recent large-$N$ predictions for the coefficients of the large-charge EFT.

Comments: 12 pages, 9 figures