Wilson Line Picture of Levin-Wen Partition Functions

Details Wilson Line Picture of Levin-Wen Partition Functions Wilson Line Picture of Levin-Wen Partition Functions

2010-04-28

arxiv.org/abs/1004.5147v3

New J. Phys. 13 065001, 2011

Physics

Condensed Matter

Strongly Correlated Electrons

Final published version; Appendix added

Scientific paper

10.1088/1367-2630/13/6/065001

Levin and Wen [Phys. Rev. B 71, 045110 (2005)] have recently given a lattice Hamiltonian description of doubled Chern-Simons theories. We relate the partition function of these theories to an expectation of Wilson loops that form a link in 2+1 dimensional spacetime known in the mathematical literature as Chain-Mail. This geometric construction gives physical interpretation of the Levin-Wen Hilbert space and Hamiltonian, its topological invariance, exactness under coarse-graining, and how two opposite chirality sectors of the doubled theory arise.

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