Bilayer Kitaev models: Phase diagrams and novel phases

TL;DR

This paper explores the phase diagrams of bilayer Kitaev models, revealing how inter-layer coupling and anisotropy lead to various phases including novel macro-spin and flux phases, expanding understanding of quantum spin liquids.

Contribution

It introduces a detailed analysis of bilayer Kitaev models, discovering new macro-spin and flux phases, and elucidates the effects of stacking and anisotropy on phase transitions.

Findings

Destruction of topological spin liquid with increasing inter-layer coupling.

Identification of two novel macro-spin phases with classical spin liquid behavior.

Evidence for a flux phase with spontaneous inter-layer coherence.

Abstract

Kitaev's honeycomb-lattice spin-$1/2$ model has become a paradigmatic example for $\mathbb{Z}_2$ quantum spin liquids, both gapped and gapless. Here we study the fate of these spin-liquid phases in differently stacked bilayer versions of the Kitaev model. Increasing the ratio between the inter-layer Heisenberg coupling $J_\perp$ and the intra-layer Kitaev couplings $K^{x,y,z}$ destroys the topological spin liquid in favor of a paramagnetic dimer phase. We study phase diagrams as a function of $J_\perp/K$ and Kitaev coupling anisotropies using Majorana-fermion mean-field theory, and we employ different expansion techniques in the limits of small and large $J_\perp/K$. For strongly anisotropic Kitaev couplings, we derive effective models for the different layer stackings which we use to discuss the quantum phase transition out of the Kitaev phase. We find that the phase diagrams depend sensitively on the nature of the stacking and anisotropy strength. While in some stackings and at strong anisotropies we find a single transition between the Kitaev and dimer phases, other stackings are more involved: Most importantly, we prove the existence of two novel macro-spin phases which can be understood in terms of Ising chains which can be either coupled ferromagnetically or remain degenerate, thus realizing a classical spin liquid. In addition, our results suggest the existence of a flux phase with spontaneous inter-layer coherence.