Exactly solvable Kitaev model in three dimensions

TL;DR

This paper introduces an exactly solvable three-dimensional generalization of the Kitaev model, revealing a phase diagram with gapped and gapless phases, and characterizing flux excitations as loop structures on a pyrochlore-like lattice.

Contribution

It presents a new 3D Kitaev model, solves it exactly, and analyzes its phase diagram, flux excitations, and low-energy effective Hamiltonian, extending the 2D Kitaev model insights.

Findings

Identifies gapped and gapless phases in the 3D model.

Flux excitations form loop structures on a pyrochlore lattice.

Gapless phase features a contour where the gap vanishes in k-space.

Abstract

We introduce a spin-1/2 model in three dimensions which is a generalization of the well-known Kitaev model on a honeycomb lattice. Following Kitaev, we solve the model exactly by mapping it to a theory of non-interacting fermions in the background of a static Z_2 gauge field. The phase diagram consists of a gapped phase and a gapless one, similar to the two-dimensional case. Interestingly, unlike in the two-dimensional model, in the gapless phase the gap vanishes on a contour in the k space. Furthermore, we show that the flux excitations of the gauge field, due to some local constraints, form loop like structures; such loops exist on a lattice formed by the plaquettes in the original lattice and is topologically equivalent to the pyrochlore lattice. Finally, we derive a low-energy effective Hamiltonian that can be used to study the properties of the excitations in the gapped phase.