Fidelity susceptibility near topological phase transitions in quantum walks

TL;DR

This paper links fidelity susceptibility with curvature functions in topological phase transitions, using quantum walks to accurately capture critical behavior and scaling laws in Dirac models.

Contribution

It reveals that fidelity susceptibility equals the curvature function in topological transitions, and demonstrates this in quantum walk simulations of Dirac models.

Findings

Fidelity susceptibility coincides with the curvature function in topological transitions.

Quantum walks accurately capture critical exponents and scaling laws.

Correlation length from the curvature function indicates the decay scale of fidelity susceptibility.

Abstract

The notion of fidelity susceptibility, introduced within the context of quantum metric tensor, has been an important quantity to characterize the criticality near quantum phase transitions. We demonstrate that for topological phase transitions in Dirac models, provided the momentum space is treated as the manifold of the quantum metric, the fidelity susceptibility coincides with the curvature function whose integration gives the topological invariant. Thus the quantum criticality of the curvature function near a topological phase transition also describes the criticality of the fidelity susceptibility, and the correlation length extracted from the curvature function also gives a momentum scale over which the fidelity susceptibility decays. To map out the profile and criticality of the fidelity susceptibility, we turn to quantum walks that simulate one-dimensional class BDI and two-dimensional class D Dirac models, and demonstrate their accuracy in capturing the critical exponents and scaling laws near topological phase transitions.