Theory of the Kitaev model in a [111] magnetic field

Shang-Shun Zhang,Gábor B Halász,Cristian D Batista

doi:10.1038/s41467-022-28014-3

Abstract

Recent numerical studies indicate that the antiferromagnetic Kitaev honeycomb lattice model undergoes a magnetic-field-induced quantum phase transition into a new spin-liquid phase. This intermediate-field phase has been previously characterized as a gapless spin liquid. By implementing a recently developed variational approach based on the exact fractionalized excitations of the zero-field model, we demonstrate that the field-induced spin liquid is gapped and belongs to Kitaev’s 16-fold way. Specifically, the low-field non-Abelian liquid with Chern number C = ±1 transitions into an Abelian liquid with C = ±4. The critical field and the field-dependent behaviors of key physical quantities are in good quantitative agreement with published numerical results. Furthermore, we derive an effective field theory for the field-induced critical point which readily explains the ostensibly gapless nature of the intermediate-field spin liquid.

Highlights

Recent numerical studies indicate that the antiferromagnetic Kitaev honeycomb lattice model undergoes a magnetic-field-induced quantum phase transition into a new spin-liquid phase
While the ferromagnetic Kitaev model has a single transition into a polarized phase, the antiferromagnetic Kitaev model includes a new intermediate-field spin liquid between the low-field non-Abelian spin liquid[1] and the high-field polarized phase
Since a spin excitation fractionalizes into a pair of fermion excitations, and the fermions at h = hc are gapless at the Γ point, a pair of gapless fermions has zero total momentum, corresponding to a vanishing spin gap at the Γ point. These similarities between the infinite DMRG (iDMRG) results and those obtained from our effective Hamiltonian H~ indicate that our variational low-energy manifold captures the essence of the phase transition at h = hc and the new spin-liquid phase at h ≳ hc

Summary

Introduction

Recent numerical studies indicate that the antiferromagnetic Kitaev honeycomb lattice model undergoes a magnetic-field-induced quantum phase transition into a new spin-liquid phase. The effective field theory of the quantum critical point, as derived from the microscopic Hamiltonian, predicts a low-energy ring of gapped excitations in momentum space, which is difficult to be distinguished from a gapless Fermi surface in finite systems.

Results

Conclusion