Twisted Kitaev Bilayers and the Moir\'e Ising Model

TL;DR

This paper investigates twisted Kitaev bilayers, revealing that strong interlayer interactions create non-Abelian defects that enable anyon tunneling, with low-energy behavior mapped onto quantum Ising models showing phase transitions.

Contribution

It introduces a novel analysis of twisted Kitaev bilayers, demonstrating the formation of non-Abelian genon defects and their effective description via quantum Ising models.

Findings

Non-Abelian genon defects form in twisted bilayers with strong interlayer interactions.

The low-energy dynamics map onto four quantum Ising models.

Phase transition from paramagnetic to ferromagnetic occurs with increasing twist angle.

Abstract

In recent years, there have been numerous examples of twisted bilayer systems that host remarkable physical properties that are not found in their untwisted counterparts. Motivated by this, we study the properties of twisted bilayers of the Kitaev honeycomb model in the Abelian spin liquid phase. We show that for strong, short-ranged, interlayer interactions, a super-lattice of non-Abelian defects forms in the twisted bilayer system. These non-Abelian defects are wormhole-like genons that allow anyons from one layer to tunnel to the other layer. We find that when a magnetic field is applied to the system, the low energy dynamics of the twisted bilayer system can be mapped onto four quantum Ising models arising from the degrees of freedom localized on the genon defects. At small twist angles, the Ising models are in a trivial paramagnetic phase, and at large twist angles, they are in a ferromagnetic phase.