Low-energy Majorana states in spin-liquid transitions in a three-dimensional Kitaev model

TL;DR

This study numerically investigates a three-dimensional Kitaev model, revealing how thermal fluctuations influence Majorana fermion spectra and induce a transition from gapless to gapped states near the spin liquid boundary.

Contribution

It demonstrates the impact of thermal fluctuations on Majorana spectra in a 3D Kitaev model, highlighting spectrum gap opening near the phase boundary.

Findings

Majorana spectra are gapless in the spin liquid phase at low temperature.

Thermal fluctuations fill the semimetallic dip in the spectrum as temperature increases.

An excitation gap develops near the gapless-gapped boundary at the transition temperature.

Abstract

A three-dimensional Kitaev model on a hyperhoneycomb lattice is investigated numerically at finite temperature. The Kitaev model is one of the solvable quantum spin models, where the ground state is given by gapped and gapless spin liquids, depending on the anisotropy of the interactions. This model can be rewritten as a free Majorana fermion system coupled with $Z_2$ variables. The density of states of Majorana fermions shows an excitation gap in the gapped region, while it is semimetallic in the gapless region reflecting the Dirac node. Performing the Monte Carlo simulation, we calculate the temperature dependence of the Majorana spectra. We find that the semimetallic dip is filled up as temperature increases in the gapless region, but surprisingly, the spectrum develops an excitation gap in the region near the gapless-gapped boundary. Such changes of the low-energy spectrum appear sharply at the transition temperature from the spin liquid to the paramagnetic state. The results indicate that thermal fluctuations of the $Z_2$ fields significantly influence the low-energy state of Majorana fermions, especially in the spin liquid formation.