# Multicritical behavior of the fidelity susceptibility for the 2D quantum transverse-field $XY$ model

## TL;DR

This paper investigates the multicritical behavior of the fidelity susceptibility in the 2D quantum XY model with a transverse field, revealing crossover scaling near the multicritical point through finite-size analysis.

## Contribution

It provides a detailed finite-size scaling analysis of fidelity susceptibility at the multicritical point, applying crossover scaling theory to the 2D quantum XY model.

## Key findings

- Fidelity susceptibility follows crossover scaling near the multicritical point.
- Finite-size scaling analysis confirms the universality class of the phase transition.
- Results align with previous studies on multicritical behavior in quantum spin models.

## Abstract

The two-dimensional quantum $XY$ model with a transverse magnetic field was investigated with the exact diagonalization method. Upon turning on the magnetic field $h$ and the $XY$-plane anisotropy $\eta$, there appear a variety of phase boundaries, which meet at the multicritical point $(h,\eta)=(2,0)$. We devote ourselves to the Ising-universality branch, placing an emphasis on the multicritical behavior. As a probe to detect the underlying phase transitions, we adopt the fidelity susceptibility $\chi_F$. The fidelity susceptibility does not rely on any presumptions as to the order parameter involved. We made a finite-size-scaling analysis of $\chi_F$ for $\eta=1$ (Ising limit), where a number of preceding results are available. Thereby, similar analyses with $\eta$ scaled were carried out around the multicritical point. We found that the $\chi_F$ data are described by the crossover scaling theory. A comparison with the preceding studies of the multicriticality is made.