A higher dimensional generalization of the Kitaev spin liquid

TL;DR

This paper introduces a four-dimensional exactly solvable Kitaev spin liquid model with unique Fermi surface features and flux properties, advancing understanding of higher-dimensional fractionalization.

Contribution

It presents the first four-dimensional Kitaev spin liquid model with explicit lattice structure and analyzes its Fermi surface and vison energy costs.

Findings

Fermi surface consists of two-dimensional surfaces.

Ground state is flux-free due to positive vison energy.

Model provides insights into higher-dimensional fractionalization.

Abstract

We construct an exactly solvable model of a four-dimensional Kitaev spin liquid. The lattice structure is orthorhombic and each unit-cell contains six sublattice degrees of freedom. We demonstrate that the Fermi surface of the model is made up of two-dimensional surfaces. Additionally, we evaluate the energy cost of creating visons using scattering theory. The positive bond-flip energy suggests that the system's ground state is flux-free, similar to the two-dimensional Kitaev honeycomb model. Our model sheds light on the realization of higher-dimensional fractionalization.