Anyonic Loops in Three Dimensional Spin liquid and Chiral Spin Liquid

Details Anyonic Loops in Three Dimensional Spin liquid and Chiral Spin Liquid Anyonic Loops in Three Dimensional Spin liquid and Chiral Spin Liquid

2007-12-27

arxiv.org/abs/0712.4231v3

Physics

Condensed Matter

Strongly Correlated Electrons

13 pages, 12 figures, final version to be published on Nucl. Phys. B

Scientific paper

10.1016/j.nuclphysb.2008.06.009

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.

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