Ground-state fidelity at first-order quantum transitions

TL;DR

This paper investigates how the fidelity and susceptibility behave near quantum phase transitions in finite systems, extending finite-size scaling analysis to first-order transitions with analytical and numerical support.

Contribution

It develops a finite-size scaling framework for fidelity at first-order quantum transitions, expanding beyond the continuous transition case.

Findings

Fidelity scaling differs qualitatively at first-order transitions.

Analytical and numerical results support the new scaling framework.

The approach applies to the quantum Ising chain under a longitudinal field.

Abstract

We analyze the scaling behavior of the fidelity, and the corresponding susceptibility, emerging in finite-size many-body systems whenever a given control parameter $\lambda$ is varied across a quantum phase transition. For this purpose we consider a finite-size scaling (FSS) framework. Our working hypothesis is based on a scaling assumption of the fidelity in terms of the FSS variables associated to $\lambda$ and to its variation $\delta \lambda$. This framework entails the FSS predictions for continuous transitions, and meanwhile enables to extend them to first-order transitions, where the FSS becomes qualitatively different. The latter is supported by analytical and numerical analyses of the quantum Ising chain along its first-order quantum transition line, driven by an external longitudinal field.