Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions

TL;DR

This paper resolves a controversy by showing that fidelity susceptibility at Berezinskii-Kosterlitz-Thouless quantum phase transitions exhibits a cusp-like peak rather than divergence, due to logarithmic corrections, supported by numerical evidence.

Contribution

It demonstrates that fidelity susceptibility does not diverge at BKT transitions but forms a cusp, clarifying previous conflicting predictions and numerical claims.

Findings

Fidelity susceptibility peaks cusp-like at the transition

No divergence of fidelity susceptibility at BKT transition

Logarithmic corrections explain previous numerical discrepancies

Abstract

We clarify the long-standing controversy concerning the behavior of the ground state fidelity in the vicinity of a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type in one-dimensional systems. Contrary to the prediction based on the Gaussian approximation of the Luttinger liquid approach, it is shown that the fidelity susceptibility does not diverge at the transition, but has a cusp-like peak $\chi_c- \chi(\lambda)\sim \sqrt{|\lambda_c-\lambda|} $, where $\lambda$ is a parameter driving the transition, and $\chi_c$ is the peak value at the transition point $\lambda=\lambda_c$. Numerical claims of the logarithmic divergence of fidelity susceptibility with the system size (or temperature) are explained by logarithmic corrections due to marginal operators, which is supported by numerical calculations for large systems.