Robust non-Abelian spin liquid and possible intermediate phase in antiferromagnetic Kitaev model with magnetic field

TL;DR

This study explores the stability of non-Abelian topological spin liquid phases in the antiferromagnetic Kitaev model under magnetic fields, revealing a robust phase and an intermediate gapless phase before polarization.

Contribution

It demonstrates the extended stability of the AFM Kitaev spin liquid under magnetic fields and identifies an intermediate gapless phase, using combined DMRG and ED methods.

Findings

AFM spin liquid remains stable up to higher fields than FM

An intermediate gapless phase appears at intermediate magnetic fields

The chiral topological phase shows remarkable stability in AFM Kitaev model

Abstract

We investigate the non-Abelian topological chiral spin liquid phase in the two-dimensional (2D) Kitaev honeycomb model subject to a magnetic field. By combining density matrix renormalization group (DMRG) and exact diagonalization (ED) we study the energy spectra, entanglement, topological degeneracy, and expectation values of Wilson loop operators, allowing for robust characterization. While the ferromagnetic (FM) Kitaev spin liquid is already destroyed by a weak magnetic field with Zeeman energy $H_*^\text{FM} \approx 0.02$, the antiferromagnetic (AFM) spin liquid remains robust up to a magnetic field that is an order of magnitude larger, $H_*^\text{AFM} \approx 0.2$. Interestingly, for larger fields $H_*^\text{AFM} < H < H_{**}^\text{AFM}$, an intermediate gapless phase is observed, before a second transition to the high-field partially-polarized paramagnet. We attribute this rich phase diagram, and the remarkable stability of the chiral topological phase in the AFM Kitaev model, to the interplay of strong spin-orbit coupling and frustration enhanced by the magnetic field. Our findings suggest relevance to recent experiments on RuCl$_3$ under magnetic fields.