Anyonic Loops in Three Dimensional Spin liquid and Chiral Spin Liquid

TL;DR

This paper introduces a class of exactly solvable three-dimensional spin liquids and chiral spin liquids with non-abelian loop excitations, revealing their topological properties and quantum entanglement characteristics.

Contribution

It constructs exactly soluble models of 3D spin liquids with non-abelian statistics and characterizes their topological and entanglement features.

Findings

Existence of stable ground states with broken time reversal symmetry.

Fractionalized loop excitations obey non-abelian statistics.

Topological correlations measure global quantum entanglement.

Abstract

We established a large class of exactly soluble spin liquids and chiral spin liquids on three dimensional helix lattices by introducing Kitaev-type's spin coupling. In the chiral spin liquids, exact stable ground states with spontaneous breaking of the time reversal symmetry are found. The fractionalized loop excitations in both the spin and chiral spin liquids obey non-abelian statistics. We characterize this kind of statistics by non-abelian Berry phase and quantum algebra relation. The topological correlation of loops is independent of local order parameter and it measures the intrinsic global quantum entanglement of degenerate ground states.