Corrections to Conformal Charge at BKT Transitions

Abstract

The conformal anomaly is key to describing the physics of interacting field theories in two dimensions, and has been shown to obtain finite-size corrections that are useful to numerical and experimental studies. At Berezinskii-Kosterlitz-Thouless transitions, the corrections are logarithmic with previously unknown universal coefficients. In this paper, I reveal the universal, $1^{st}$-order correction to the conformal anomaly for finite-sized systems at BKT transitions. This term results solely from topological defects that are irrelevant in the infrared limit. I compare the result with careful observations of entanglement for the quantum Heisenberg model with periodic boundary conditions in one spatial dimension.