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

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.

arXiv comment6 pages, 3 figures

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Cited by in corpus (8)

• Thermal fractionalization of quantum spins in a Kitaev model: $T$-linear specific heat and coherent transport of Majorana fermions
• Loop-nodal and Point-nodal Semimetals in Three-dimensional Honeycomb Lattices
• Theory of Raman response in three-dimensional Kitaev spin liquids: application to $\beta -$ and $\gamma -$Li${}_2$IrO${}_3$ compounds
• Thermal transport in a two-dimensional ${\mathbb{Z}}_2$ spin liquid
• Thermodynamics of Chiral Spin Liquids with Abelian and Non-Abelian Anyons
• Thermodynamic classification of three-dimensional Kitaev spin liquids
• Thermal Transport in a one-dimensional Z${}_2$ Spin Liquid
• Weyl and nodal ring magnons in three-dimensional honeycomb lattices