Spin correlation and Majorana spectrum in chiral spin liquids in a decorated-honeycomb Kitaev model

TL;DR

This study explores how spin correlations and excitation spectra evolve with temperature in a decorated honeycomb Kitaev model, revealing crossovers and phase transitions related to Majorana fermions and topological properties.

Contribution

It provides the first detailed analysis of temperature-dependent spin correlations and Majorana spectra in a decorated honeycomb Kitaev model with both Abelian and non-Abelian phases.

Findings

Spin correlations develop around crossover temperatures.

The excitation gap in the non-Abelian phase is fragile against thermal fluctuations.

The Abelian phase's excitation gap remains stable at finite temperatures.

Abstract

Temperature evolution of the spin correlation and excitation spectrum is investigated for a Kitaev model defined on a decorated honeycomb lattice by using the quantum Monte Carlo simulation in the Majorana fermion representation. The ground state of this quantum spin model is given by two kinds of chiral spin liquids: one is topologically trivial with Abelian anyon excitations, and the other is topologically nontrivial with non-Abelian anyon excitations. While lowering temperature, the model exhibits several crossovers in the paramagnetic state, which originate from the fractionalization of quantum spins into Majorana fermions, in addition to a phase transition associated with time reversal symmetry breaking. We show that the spin correlation develops around the crossover temperatures, whereas it shows a slight change at the critical temperature, as in other Kitaev-type models. We also calculate the excitation spectrum in terms of Majorana fermions, and find that the excitation gap in the non-Abelian phase is fragile against thermal fluctuations of the $Z_2$ fluxes, while that in the Abelian phase remains open.