Conformal dimensions via large charge expansion


We construct an efficient Monte Carlo algorithm that overcomes the severe signal-to-noise ratio problems and helps us to accurately compute the conformal dimensions of large-$Q$ fields at the Wilson-Fisher fixed point in the $O(2)$ universality class. Using it we verify a recent proposal that conformal dimensions of strongly coupled conformal field theories with a global $U(1)$ charge can be obtained via a series expansion in the inverse charge $1/Q$. We find that the conformal dimensions of the lowest operator with a fixed charge $Q$ are almost entirely determined by the first few terms in the series.

Phys.Rev.Lett. 120 (2018) no.6, 061603