Universal fidelity near quantum and topological phase transitions in finite 1D systems

TL;DR

This paper investigates the behavior of quantum fidelity near phase transitions in finite 1D systems, providing analytical formulas and numerical validation for various boundary conditions and topological states.

Contribution

It offers new analytical expressions for fidelity susceptibility in finite 1D systems, accounting for different boundary conditions and edge states, and explores their impact on phase transition signatures.

Findings

Analytical formulas for fidelity susceptibility derived for various boundary conditions.

Edge states significantly influence the fidelity susceptibility both quantitatively and qualitatively.

Numerical data supports the analytical results across different system configurations.

Abstract

We study the quantum fidelity (groundstate overlap) near quantum phase transitions of the Ising universality class in one dimensional (1D) systems of finite size L. Prominent examples occur in magnetic systems (e.g. spin-Peierls, the anisotropic XY model), and in 1D topological insulators of any topologically nontrivial Altland-Zirnbauer-Kitaev universality class. The rescaled fidelity susceptibility is a function of the only dimensionless parameter LM, where 2M is the gap in the fermionic spectrum. We present analytic expressions for the fidelity susceptibility for periodic and open boundaries conditions with zero, one or two edgestates. The latter are shown to have a crucial impact and alter the susceptibility both quantitatively and qualitatively. We support our analytical solutions with numerical data.