Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model

TL;DR

This paper investigates the Kitaev honeycomb model, demonstrating how fidelity susceptibility signals topological phase transitions and analyzing correlation decay, revealing critical behavior at phase boundaries.

Contribution

It provides an exact analysis of fidelity susceptibility and bond correlations, linking them to topological phase transitions in the Kitaev honeycomb model.

Findings

Fidelity susceptibility detects topological phase transition.

Exponential decay of correlations in gapped phase.

Algebraic decay of correlations in gapless phase.

Abstract

We study exactly both the ground-state fidelity susceptibility and bond-bond correlation function in the Kitaev honeycomb model. Our results show that the fidelity susceptibility can be used to identify the topological phase transition from a gapped A phase with Abelian anyon excitations to a gapless B phase with non-Abelian anyon excitations. We also find that the bond-bond correlation function decays exponentially in the gapped phase, but algebraically in the gapless phase. For the former case, the correlation length is found to be $1/\xi=2\sinh^{-1}[\sqrt{2J_z -1}/(1-J_z)]$, which diverges around the critical point $J_z=(1/2)^+$.