# Three-dimensional topological lattice models with surface anyons

@article{Keyserlingk2012ThreedimensionalTL,
title={Three-dimensional topological lattice models with surface anyons},
author={C. W. von Keyserlingk and Fiona J. Burnell and Steven H. Simon},
journal={Physical Review B},
year={2012},
volume={87},
pages={045107}
}
• Published 25 August 2012
• Physics
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## References

SHOWING 1-10 OF 44 REFERENCES

• Physics
• 2011
We construct exactly soluble lattice models for fractionalized, time reversal invariant electronic insulators in 2 and 3 dimensions. The low energy physics of these models is exactly equivalent to a
• Physics
• 2007
We construct an exactly solvable Hamiltonian acting on a 3-dimensional lattice of spin-$\frac 1 2$ systems that exhibits topological quantum order. The ground state is a string-net and a membrane-net
• Physics
• 2012
Time-reversal invariant three-dimensional topological insulators can be defined fundamentally by a topological field theory with a quantized axion angle theta of zero or pi. It was recently shown
• Physics
• 2011
We describe a family of phase transitions connecting phases of differing non-trivial topological order by explicitly constructing Hamiltonians of the Levin-Wen[PRB 71, 045110] type which can be
• Physics
• 2005
We show that quantum systems of extended objects naturally give rise to a large class of exotic phases---namely topological phases. These phases occur when extended objects, called `string-nets,''
• Physics
Physical review letters
• 2010
This work introduces the concept of fractional topological insulator defined by a fractional axion angle and shows that it can be consistent with time reversal T invariance if ground state degeneracies are present.
An interacting bosonic model of Kitaev type is proposed on the three-dimensional diamond lattice. Similarly to the two-dimensional Kitaev model on the honeycomb lattice, which exhibits both Abelian
• Physics
• 2008
We systematically study topological phases of insulators and superconductors (or superfluids) in three spatial dimensions. We find that there exist three-dimensional (3D) topologically nontrivial