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2007

Quantum loop models and the non-abelian toric code

Fendley, Paul

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I define quantum loop models whose degrees of freedom are Ising spins on the square lattice as in the toric code, but where the excitations should have non-abelian statistics.

The inner product is topological, allowing a direct implementation of the anyonic fusion matrix on the lattice.
It also makes deconfined anyons possible for a variety of values of the weight per loop $d$ in the ground state.
For d=\sqrt{2}, a gapped non-abelian topological phase can occur with only four-spin interactions.

Quantum loop models and the non-abelian toric code · Around

Built on

C.M. Fortuin and P.W. Kasteleyn, Physica 57
1972
Earlier work this paper cites.
B. Nienhuis in Phase Transitions and Critical Phenomena
1987
Earlier work this paper cites.
D. Rokhsar and S. Kivelson, Phys. Rev. Lett. 61
1988
Earlier work this paper cites.

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see S. Das Sarma, M. Freedman, C. Nayak, S.H. Simon, A. Stern, arXiv:0707.1889 and references therein
Original
Cited in the paper.
M. Levin, unpublished
Cited in the paper.
P. Fendley and V. Krushkal, “Link invariants and the chromatic polynomial”, to appear
Cited in the paper.
P. Fendley and J. Jacobsen, to appear
Original
Cited in the paper.

Then

M. Freedman, C. Nayak and K. Shtengel, Phys. Rev. Lett. 94
2005
Later among the works it cites.
M.A. Levin and X.-G. Wen, Phys. Rev. B 71
2005
Later among the works it cites.

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