Majorana Fermion Mean-Field Theories of Kitaev Quantum Spin Liquids

Abstract

We determine the phase diagrams of anisotropic Kitaev-Heisenberg models on the honeycomb lattice using parton mean-field theories based on different Majorana fermion representations of the $S=1/2$ spin operators. Firstly, we use a two-dimensional Jordan-Wigner transformation (JWT) involving a semi-infinite snake string operator. In order to ensure that the fermionized Hamiltonian remains local we consider the limit of extreme Ising exchange anisotropy in the Heisenberg sector. Secondly, we use the conventional Kitaev representation in terms of four Majorana fermions subject to local constraints, which we enforce through Lagrange multipliers. For both representations we self-consistently decouple the interaction terms in the bond and magnetization channels and determine the phase diagrams as a function of the anisotropy of the Kitaev couplings and the relative strength of the Ising exchange. While both mean-field theories produce identical phase boundaries for the topological phase transition between the gapless and gapped Kitaev quantum spin liquids, the JWT fails to correctly describe the the magnetic instability and finite-temperature behavior. Our results show that the magnetic phase transition is first order at low temperatures but becomes continuous above a certain temperature. At this energy scale we also observe a finite temperature crossover on the quantum spin-liquid side, from a fractionalized paramagnet at low temperatures, in which gapped flux excitations are frozen out, to a conventional paramagnet at high temperatures.

11 pages, 8 figures, accepted version

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Cited by in corpus (5)

• Probing Majorana wavefunctions in Kitaev honeycomb spin liquids with second-order two-dimensional spectroscopy
• Phonon Dynamics in the Chiral Kitaev Spin Liquid
• Nature of Topological Phase Transition of Kitaev Quantum Spin Liquids
• Topology-driven deconfined quantum criticality in magnetic bilayers
• Spin-Spin Correlations in the Kitaev Model at Finite Temperatures: Approximate and Exact Results via Green's Function Equation of Motion