Dumbbell Fermions and Spin Models on Honeycomb Lattices

TL;DR

This paper generalizes Kitaev's honeycomb spin model solution by framing it as a duality with Majorana fermions, enabling the exact solution of a broad class of spin models with various couplings and magnetic fields.

Contribution

It introduces a higher-dimensional duality framework that extends Kitaev's exact solution to more general spin models on honeycomb lattices.

Findings

Exact solutions for generalized honeycomb spin models

Infinite family of single-particle fermion equations derived

Framework unifies various solvable spin models

Abstract

We express Kitaev's exact solution of spin models on the honeycomb lattice as a special case of a higher dimensional duality between staggered Majorana fermions and Pauli spins. General models with bilinear nearest neighbor couplings of spins and external magnetic fields are soluble in this way. Each model gives rise to an infinite number of single particle fermion Schrodinger equations, depending on the choice of discrete gauge field flux.