Fidelity in topological quantum phases of matter

TL;DR

This paper demonstrates that fidelity susceptibility effectively identifies phase boundaries and critical behavior in topological quantum phases, including spin systems and topological insulator/superconductor transitions, without relying on local order parameters.

Contribution

It extends the fidelity approach to topological quantum phase transitions, providing a new tool for characterizing these phases and their critical points.

Findings

Fidelity susceptibility detects phase boundaries in 2D and 3D topological spin systems.

It reveals critical exponents related to correlation length at topological transitions.

The method applies to topological insulator/superconductor phase boundaries.

Abstract

Quantum phase transitions that take place between two distinct topological phases remain an unexplored area for the applicability of the fidelity approach. Here, we apply this method to spin systems in two and three dimensions and show that the fidelity susceptibility can be used to determine the boundary between different topological phases particular to these models, while at the same time offering information about the critical exponent of the correlation length. The success of this approach relies on its independence on local order parameters or breaking symmetry mechanisms, with which non-topological phases are usually characterized. We also consider a topological insulator/superconducting phase transition in three dimensions and point out the relevant features of fidelity susceptibility at the boundary between these phases.