Fidelity spectrum and phase transitions of quantum systems

Abstract

Quantum fidelity between two density matrices, $F({\rho }_1,{\rho }_2)$ is usually defined as the trace of the operator $\mathcal{F}=\sqrt{\sqrt{{\rho }_1}{\rho }_2\sqrt{{\rho }_1}}$. 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.

12 figures

References in corpus (12)

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• The three site interacting spin chain in staggered field: Fidelity vs Loschmidt echo
• Role of marginality in quantum fidelity and Loschmidt echo: Dirac points in 2-D
• Vanishing k-space fidelity and phase diagram's bulk-edge-bulk correspondence
• Information geometric analysis of long range topological superconductors
• Witnessing criticality in non-Hermitian systems via entropic uncertainty relation