Fidelity analysis of topological quantum phase transitions

TL;DR

This paper uses the fidelity metric to analyze topological quantum phase transitions, demonstrating divergences at critical points and highlighting the method's usefulness for characterizing phases without local order parameters.

Contribution

It introduces a fidelity-based approach to study topological phase transitions and leverages classical mappings to analyze critical scaling behavior.

Findings

Fidelity metric diverges at topological phase boundaries

Mapping to classical models aids in understanding critical scaling

Fidelity approach effectively characterizes topological phases

Abstract

We apply the fidelity metric approach to analyze two recently introduced models that exhibit a quantum phase transition to a topologically ordered phase. These quantum models have a known connection to classical statistical mechanical models; we exploit this mapping to obtain the scaling of the fidelity metric tensor near criticality. The topological phase transitions manifest themselves in divergences of the fidelity metric across the phase boundaries. These results provide evidence that the fidelity approach is a valuable tool to investigate novel phases lacking a clear characterization in terms of local order parameters.