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}
}
We study a class of three dimensional exactly solvable models of topological matter first put forward by Walker and Wang [arXiv:1104.2632v2]. While these are not models of interacting fermions, they may well capture the topological behavior of some strongly correlated systems. In this work we give a full pedagogical treatment of a special simple case of these models, which we call the 3D semion model: We calculate its ground state degeneracies for a variety of boundary conditions, and classify… 

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References

SHOWING 1-10 OF 44 REFERENCES

Exactly soluble models for fractional topological insulators in two and three dimensions

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

Exact topological quantum order in D=3 and beyond : Branyons and brane-net condensates

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

Models of three-dimensional fractional topological insulators

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

Condensation of achiral simple currents in topological lattice models: Hamiltonian study of topological symmetry breaking

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

String-net condensation: A physical mechanism for topological phases

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,''

Fractional topological insulators in three dimensions.

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.

Three-dimensional topological phase on the diamond lattice

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

Classification of topological insulators and superconductors in three spatial dimensions

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