Revealing divergent length scales using quantum Fisher information in the Kitaev honeycomb model

TL;DR

This paper investigates how quantum Fisher information reveals different length scales at quantum phase transitions in the Kitaev honeycomb model, highlighting divergent behaviors linked to local operators and phase boundaries.

Contribution

It introduces a detailed analysis of quantum Fisher information's divergence at phase transitions, connecting it to local operator behavior and length scales in the Kitaev model.

Findings

Divergent second derivatives of QFI at critical points.

Different QFI behaviors depending on local operators and phase side.

Link between QFI divergence and diverging correlation length scales.

Abstract

We compute the quantum Fisher information (QFI) associated with two different local operators in the Kitaev honeycomb model, and find divergent behaviour in the second derivatives of these quantities with respect to the driving parameter at the quantum phase transition between the gapped and gapless phases for both fully anti-ferromagnetic and fully ferromagnetic exchange couplings. The QFI associated with a local magnetization operator behaves differently from that associated with a local bond operator depending on whether the critical point is approached from the gapped or gapless side. We show how the behaviour of the second derivative of the QFI at the critical point can be understood in terms of diverging length scales in the correlators of the local generators.