Corrections to Conformal Charge at BKT Transitions

TL;DR

This paper derives the universal first-order correction to the conformal anomaly at BKT transitions, highlighting the role of topological defects and validating results through entanglement measurements in the quantum Heisenberg model.

Contribution

It introduces the first-order correction to the conformal anomaly at BKT transitions, linking it to topological defects and providing a comparison with numerical entanglement data.

Findings

Universal first-order correction derived for BKT transitions

Correction originates from irrelevant topological defects

Validation through entanglement measurements in quantum Heisenberg model

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.