# Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition

## TL;DR

This paper demonstrates that the fidelity susceptibility peak in the Berezinskii-Kosterlitz-Thouless transition shifts away from the critical point, with a universal shape linked to the correlation length, supported by numerical simulations.

## Contribution

It reveals a universal shift of the fidelity susceptibility peak from the critical point in BKT transitions, contrasting with conventional continuous quantum critical points.

## Key findings

- Peak shift from J_c to J^* is proportional to transition width B^2.
- Universal peak shape correlates with the correlation length.
- Numerical simulations confirm the shift in Bose-Hubbard and spin-3/2 XXZ models.

## Abstract

We show that the peak which can be observed in fidelity susceptibility around the Berezinskii-Kosterlitz-Thouless transition is shifted from the quantum critical point (QCP) at $J_c$ to $J^*$ in the gapped phase by a value $|J^* - J_c| = B^2/36$, where $B^2$ is a transition width controlling the asymptotic form of the correlation length $\xi \sim \exp(-B/\sqrt{|J-J_c|})$ in that phase. This is in contrast to the conventional continuous QCP where the maximum is an indicator of the position of the critical point. The shape of the peak is universal, emphasizing the close connection between fidelity susceptibility and the correlation length. We support those arguments with numerical matrix product state simulations of the one-dimensional Bose-Hubbard model in the thermodynamic limit, where the broad peak is located at $J^*=0.212$ that is significantly different from $J_c=0.3048(3)$. In the spin-$3/2$ XXZ model the shift from $J_c=1$ to $J^*=1.0021$ is small but the narrow universal peak is much more pronounced over the non-universal background.