# Ground-state degeneracy of topological phases on open surfaces.

@article{Hung2015GroundstateDO, title={Ground-state degeneracy of topological phases on open surfaces.}, author={Ling-Yan Hung and Yidun Wan}, journal={Physical review letters}, year={2015}, volume={114 7}, pages={ 076401 } }

We relate the ground state degeneracy of a non-Abelian topological phase on a surface with boundaries to the anyon condensates that break the topological phase into a trivial phase. Specifically, we propose that gapped boundary conditions of the surface are in one-to-one correspondence with the sets of condensates, each being able to completely break the phase, and we substantiate this by examples. The ground state degeneracy resulting from a particular boundary condition coincides with the… Expand

#### 47 Citations

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Abstract
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#### References

SHOWING 1-10 OF 15 REFERENCES

Phys

- Rev. B 30, 1097
- 1984

Phys

- Rev. Lett. 50, 1395
- 1983

Int

- J. Mod. Phys. B p. 1450172
- 2014

p

- 11
- 2014

Phys

- Rev. X 3, 021009
- 2013

Phys

- Rev. B 87, 125114
- 2013

Phys

- Rev. B 87, 155115
- 2013

Commun

- Math. Phys. 313, 351
- 2012

Phys

- Rev. B 79, 045316
- 2009

Phys

- Rev. Lett. 102, 220403
- 2009