Ground-state fidelity at first-order quantum transitions

Davide Rossini, Ettore Vicari

Published 2018-07-04Version 1

We propose a finite-size scaling (FSS) theory for the fidelity, and the corresponding susceptibility, that holds whenever a given control parameter $\lambda$ is varied across a quantum phase transition. 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.