Entanglement modes and topological phase transitions in superconductors

TL;DR

This paper demonstrates how quantum information measures like entanglement spectrum and fidelity can identify and distinguish topological phases and phase transitions in a 2D p-wave superconductor with spin-orbit coupling and Zeeman effects.

Contribution

It introduces quantum information tools to detect topological phases and transitions in superconductors, providing a new perspective on their characterization.

Findings

Entanglement spectrum eigenvectors align with triplet pairing in topological phases.

Fidelity spectrum signals phase transitions in the parameter space.

Quantum information measures effectively distinguish topological phases.

Abstract

Topological insulators and topological superconductors display various topological phases that are characterized by different Chern numbers or by gapless edge states. In this work we show that various quantum information methods such as the von Neumann entropy, entanglement spectrum, fidelity, and fidelity spectrum may be used to detect and distinguish topological phases and their transitions. As an example we consider a two-dimensional $p$-wave superconductor, with Rashba spin-orbit coupling and a Zeeman term. The nature of the phases and their changes are clarified by the eigenvectors of the $k$-space reduced density matrix. We show that in the topologically nontrivial phases the highest weight eigenvector is fully aligned with the triplet pairing state. A signature of the various phase transitions between two points on the parameter space is encoded in the $k$-space fidelity operator.