Kitaev model in a magnetic field: stable emergent structure, degenerate classical ground states, and reentrant topology

TL;DR

This study explores the Kitaev model under magnetic fields, revealing stable emergent structures, degenerate classical ground states, and reentrant topological phases, supported by mean-field and exact diagonalization analyses.

Contribution

It provides new insights into the phase diagram of the Kitaev model under magnetic fields, including emergent phenomena and reentrant topology, extending understanding of quantum spin liquids.

Findings

Emergent fields stabilize direction-dependently under magnetic fields.

Two distinct intermediate phases with different topological and classical properties.

Reentrant topological behavior in the anisotropic Kitaev model under magnetic fields.

Abstract

We have studied the anti-ferromagnetic Kitaev model on a honeycomb lattice under the Zeeman field, using an extensive Majorana mean-field analysis. When the magnetic field is along a specific Cartesian axis, we find that the emergent fields exhibit direction-dependent stabilization up to a certain critical strength of the external field. For a conical magnetic field, the characteristics of the emergent intermediate state are elusive. Our mean-field analysis reveals the existence of two distinct phases in the intermediate region. First, the system enters a disordered phase, where emergent-field densities converge to random values, and the Chern number is ill-defined. The magnitude of magnetization also fluctuates and remains less than unity, indicating a strong quantum effect. In the second phase, emergent-field densities attain vanishingly small values. In this phase, the magnetization components fluctuate heavily, but the magnitude of the magnetization vectors becomes unity, indicating highly degenerate classical ground states. We perform exact diagonalization calculations that qualitatively support some of the mean-field results. We extend our study to the anisotropic limit of the Kitaev coupling parameters. When the couplings are beyond the triangular inequality, the pure Kitaev model is known to host a topologically trivial gapped quantum spin liquid. We find that, for intermediate strengths of a conical magnetic field, topology shows a reentrant behavior.