Fidelity spectrum and phase transitions of quantum systems

TL;DR

This paper introduces the fidelity spectrum, derived from quantum fidelity, as a new tool to analyze phase transitions and characterize different phases in many-body quantum systems.

Contribution

It studies the logarithmic spectrum of the fidelity operator in various quantum systems, linking it to entanglement spectrum and phase characterization.

Findings

Fidelity spectrum reduces to entanglement spectrum when states are equal.

Fidelity spectrum helps distinguish different quantum phases.

Application to spin chains and superconductors demonstrates its utility.

Abstract

Quantum fidelity between two density matrices, $F(\rho_1,\rho_2)$ is usually defined as the trace of the operator ${\cal F}=\sqrt{\sqrt{\rho_1} \rho_2 \sqrt{\rho_1}}$. We study the logarithmic spectrum of this operator, which we denote by {\it fidelity spectrum}, in the cases of the $XX$ spin chain in a magnetic field, a magnetic impurity inserted in a conventional superconductor and a bulk superconductor at finite temperature. When the density matrices are equal, $\rho_1=\rho_2$, the fidelity spectrum reduces to the entanglement spectrum. We find that the fidelity spectrum can be a useful tool in giving a detailed characterization of different phases of many-body quantum systems.