Topological Quantum Liquids with Quaternion Non-Abelian Statistics

Details Topological Quantum Liquids with Quaternion Non-Abelian Statistics Topological Quantum Liquids with Quaternion Non-Abelian Statistics

2010-12-27

arxiv.org/abs/1012.5671v3

Phys. Rev. Lett. 108, 047202 (2012)

Physics

Condensed Matter

Strongly Correlated Electrons

5 pages, 3 figures

Scientific paper

Noncollinear magnetic order is typically characterized by a "tetrad" ground state manifold (GSM) of three perpendicular vectors or nematic-directors. We study three types of tetrad orders in two spatial dimensions, whose GSMs are SO(3) = S^3/Z_2, S^3/Z_4, and S^3/Q_8, respectively. Q_8 denotes the non-Abelian quaternion group with eight elements. We demonstrate that after quantum disordering these three types of tetrad orders, the systems enter fully gapped liquid phases described by Z_2, Z_4, and non-Abelian quaternion gauge field theories, respectively. The latter case realizes Kitaev's non-Abelian toric code in terms of a rather simple spin-1 SU(2) quantum magnet. This non-Abelian topological phase possesses a 22-fold ground state degeneracy on the torus arising from the 22 representations of the Drinfeld double of Q_8.

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