Fidelity susceptibility and general quench near an anisotropic quantum critical point

TL;DR

This paper investigates how fidelity susceptibility scales near anisotropic quantum critical points, revealing unique behaviors and proposing scaling relations for quench-induced heat and defect densities, validated through analytical and numerical methods.

Contribution

It introduces the scaling behavior of fidelity susceptibility at anisotropic quantum critical points and connects it to quench dynamics, providing new insights into anisotropic quantum phase transitions.

Findings

Fidelity susceptibility scales differently along parallel and perpendicular directions.

Maximum fidelity susceptibility exhibits a crossover in scaling behavior.

Scaling relations for heat and defect densities are established and verified.

Abstract

We study the scaling behavior of fidelity susceptibility density $(\chi_{\rm f})$ at or close to an anisotropic quantum critical point characterized by two different correlation length exponents $\nu_{||}$ and $\nu_{\bot}$ along parallel and perpendicular spatial directions, respectively. Our studies show that the response of the system due to a small change in the Hamiltonian near an anisotropic quantum critical point is different from that seen near an isotropic quantum critical point. In particular, for a finite system with linear dimension $L_{||}$ ($L_{\bot}$) in the parallel (perpendicular) directions, the maximum value of $\chi_{\rm f}$ is found to increases in a power-law fashion with $L_{||}$ for small $L_{||}$, with an exponent depending on both $\nu_{||}$ and $\nu_{\bot}$ and eventually crosses over to a scaling with $L_{\bot}$ for $L_{||}^{1/\nu_{||}} \gtrsim L_{\bot}^{1/\nu_{\bot}}$. We also propose scaling relations of heat density and defect density generated following a quench starting from an anisotropic quantum critical point and connect them to a generalized fidelity susceptibility. These predictions are verified exactly both analytically and numerically taking the example of a Hamiltonian showing a semi-Dirac band-crossing point.