Singularities in ground state fidelity and quantum phase transitions for the Kitaev model

TL;DR

This paper demonstrates that the ground state fidelity per lattice site effectively detects quantum phase transitions in the Kitaev model, revealing non-analytic behavior at phase boundaries and enabling extraction of critical exponents through finite size scaling.

Contribution

It introduces the use of ground state fidelity per lattice site to identify phase transitions and analyze critical behavior in the Kitaev model with topological order.

Findings

Fidelity per lattice site is non-analytic at phase boundaries.

Second derivative of the fidelity logarithm diverges logarithmically.

Finite size scaling yields the correlation length critical exponent.

Abstract

The ground state fidelity per lattice site is shown to be able to detect quantum phase transitions for the Kitaev model on the honeycomb lattice, a prototypical example of quantum lattice systems with topological order. It is found that, in the thermodynamic limit, the ground state fidelity per lattice site is non-analytic at the phase boundaries: the second-order derivative of its logarithmic function with respect to a control parameter describing the interaction between neighboring spins is logarithmically divergent. A finite size scaling analysis is performed, which allows us to extract the correlation length critical exponent from the scaling behaviors of the ground state fidelity per lattice site.