Intermediate gapless phase and topological phase transition of the Kitaev model in a uniform magnetic field

Abstract

We study the Kitaev model in a [001] magnetic field employing the mean field theory in the Majorana fermion representation. The mean field Hamiltonian of the system has the Bogoliubov de-Gennes (BdG) form of a 2D superconductor. We discover a robust gapless regime in intermediate magnetic field for both gapless and gapped anti-ferromagnetic Kitaev model with Jx = Jy before the system is polarized in high magnetic field. A topological phase transition connecting two gapless phases with a nodal line phase takes place at a critical magnetic field hc 1 in this regime. While the nodal line phase at hc 1 disappears when the mirror symmetry Jx = Jy is broken, the nodal point gapless phase can exist at intermediate fields even without the mirror symmetry. We reveal that the phase evolution of the system in the magnetic field is driven by the competition between the magnetic field and the particle-hole asymmetry of the normal state of the BdG Hamiltonian, which results in the robust intermediate gapless phase for the anti-ferromagnetic case. For ferromagnetic case, there is no intermediate phase transition before polarization. The above phase diagrams are confirmed by dynamical mean field theory results. arXiv:1806.04184v2 [cond-mat.str-el] 3 Sep 2018

Theory of the field-revealed Kitaev spin liquid

“…While the observation of a half-integer quantized thermal Hall conductivity is the first experimental evidence of charge-neutral non-Abelian anyons in spin systems, a microscopic theory describing their appearance under a field in α -RuCl 3 is missing. This is because, if the dominant interaction in α -RuCl 3 is the ferromagnetic (FM) Kitaev term (as shown through ab-initio studies 25,26 and spin wave analysis 36 ), the FM Kitaev phase is almost immediately destroyed, and the polarized state appears in an applied field 38–40 with no intervening phase. This can be contrasted with the antiferromagnetic (AFM) Kitaev model which hosts a potentially gapless spin liquid under a field, supported by several numerical studies 39–47 .…”

Unquantized thermal Hall effect in quantum spin liquids with spinon Fermi surfaces

“…In this work, we analyzed the thermal Hall conductivity in two important models of quantum magnets-the Kitaev honeycomb lattice model and the J 1 -J 2 -J 3 Heisenberg magnet on the triangular lattice. We paid special attention to the impact of the magnetic field, taking into account that it can drive the gapped QSL phases these systems harbor into gapless QSLs with spinon Fermi surfaces, as indicated by recent numerical studies [59][60][61][62][63][64][65]97]. For our computations, we employed a mean-field description of these phases, based on fermionic spinons, that is constrained by the aforementioned numerics and a PSG analysis.…”

“…This points toward a scenario where the effect of the field yields an additional U(1) QSL phase [58]. Indeed a plethora of numerical studies [59][60][61][62][63][64][65] indicate the presence of an intermediate gapless phase with spinon Fermi surfaces (SFS), between the gapped topological order and the trivial polarized phase at very strong fields.…”

Thermally enhanced Majorana-mediated spin transport in the Kitaev model

“…where β = 1/T , T is the temperature, Z 0 (= Tr e −βH0 ) is the partition function and Ô(t) = U † (t) ÔU (t) with the time-evolution operator U (t). At zero temperature (T = 0), the localized Z 2 fluxes freeze into the fluxfree state, and the Majorana mean-field approach should work to evaluate the expectation values [13,15,[33][34][35].…”