Chiral Spin Liquids at Finite Temperature in a Three-Dimensional Kitaev Model

TL;DR

This paper investigates three-dimensional chiral spin liquids in a Kitaev model extension, revealing distinct phase transition behaviors and exotic flux configurations through unbiased Monte Carlo simulations.

Contribution

It introduces a 3D Kitaev model on the hypernonagon lattice, deriving effective models in different limits and analyzing their phase transitions and flux degeneracies.

Findings

First-order phase transition to CSL with symmetry breaking

Unfrustrated and frustrated flux interactions lead to different CSL types

Exotic flux degeneracy and directional order in frustrated case

Abstract

Chiral spin liquids (CSLs) in three dimensions and thermal phase transitions to paramagnet are studied by unbiased Monte Carlo simulations. For an extension of the Kitaev model to a three-dimensional tricoordinate network dubbed the hypernonagon lattice, we derive low-energy effective models in two different anisotropic limits. We show that the effective interactions between the emergent $Z_2$ degrees of freedom called fluxes are unfrustrated in one limit, while highly frustrated in the other. In both cases, we find a first-order phase transition to the CSL, where both time-reversal and parity symmetries are spontaneously broken. In the frustrated case, however, the CSL state is highly exotic --- the flux configuration is subextensively degenerate while showing a directional order with broken $C_3$ rotational symmetry. Our results provide two contrasting archetypes of CSLs in three dimensions, both of which allow approximation-free simulation for the thermodynamics.