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N. Read and E. Rezayi, Phys. Rev. B 59
1999
Earlier work this paper cites.
A. Cappelli, L. S. Georgiev, and I. T. Todorov, Nuclear Physics B 599
2001
Earlier work this paper cites.
A. Kitaev, Ann. Phys. 303
2003
Earlier work this paper cites.
F. Verstraete and J. I. Cirac, Phys. Rev. A 70
2004
Earlier work this paper cites.
M. A. Levin and X.-G. Wen, Phys. Rev. B 71
2005
Earlier work this paper cites.
F. Verstraete, M. M. Wolf, D. Perez-Garcia, and J. I. Cirac, Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
F. Bais and J. Slingerland, Phys. Rev. B 79
Original
2009
Earlier work this paper cites.
O. Buerschaper, M. Aguado, and G. Vidal, Phys. Rev. B 79
Original
2009
Earlier work this paper cites.
Z.-C. Gu, M. Levin, B. Swingle, and X.-G. Wen, Phys. Rev. B 79
Original
2009
Earlier work this paper cites.

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N. Schuch, I. Cirac, and D. Pérez-García, Ann. Phys. 325
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Then

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2013
Later among the works it cites.
I. S. Eliëns, J. C. Romers, and F. A. Bais, Phys. Rev. B 90
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2014
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B. Paredes, (2014), arXiv:1402.3567
Original
2014
Later among the works it cites.
M. B. Sahinoglu, D. Williamson, N. Bultinck, M. Marien, J. Haegeman, N. Schuch, and F. Verstraete, (2014), arXiv:1409.2150
Original
2014
Later among the works it cites.
N. Bultinck, M. Mariën, D. J. Williamson, M. B. Şahinoğlu, J. Haegeman, and F. Verstraete, (2015), arXiv:1511.08090
Original

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2016

Constructing topological models by symmetrization: A PEPS study

Fernandez-Gonzalez, Carlos, Mong, Roger S. K., Landon-Cardinal, Olivier et al.

Understand

Symmetrization of topologically ordered wavefunctions is a powerful method for constructing new topological models.

Here, we study wavefunctions obtained by symmetrizing quantum double models of a group $G$ in the Projected Entangled Pair States (PEPS) formalism.
We show that symmetrization naturally gives rise to a larger symmetry group $\tilde G$ which is always non-abelian.
We prove that by symmetrizing on sufficiently large blocks, one can always construct wavefunctions in the same phase as the double model of $\tilde G$.

Built on

N. Read and E. Rezayi, Phys. Rev. B 59
1999
Earlier work this paper cites.
A. Cappelli, L. S. Georgiev, and I. T. Todorov, Nuclear Physics B 599
2001
Earlier work this paper cites.
A. Kitaev, Ann. Phys. 303
2003
Earlier work this paper cites.
F. Verstraete and J. I. Cirac, Phys. Rev. A 70
2004
Earlier work this paper cites.
M. A. Levin and X.-G. Wen, Phys. Rev. B 71
2005
Earlier work this paper cites.
F. Verstraete, M. M. Wolf, D. Perez-Garcia, and J. I. Cirac, Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
F. Bais and J. Slingerland, Phys. Rev. B 79
Original
2009
Earlier work this paper cites.
O. Buerschaper, M. Aguado, and G. Vidal, Phys. Rev. B 79
Original
2009
Earlier work this paper cites.
Z.-C. Gu, M. Levin, B. Swingle, and X.-G. Wen, Phys. Rev. B 79
Original
2009
Earlier work this paper cites.

Similar

N. Schuch, I. Cirac, and D. Pérez-García, Ann. Phys. 325
Original
2010
Cited alongside, same era.
H. Bombin, Phys. Rev. Lett. 105
Original
2010
Cited alongside, same era.
M. Barkeshli and X.-G. Wen, Phys. Rev. B 81
Original
2010
Cited alongside, same era.
N. Schuch, D. Perez-Garcia, and I. Cirac, Phys. Rev. B 84
Original
2011
Cited alongside, same era.
B. Paredes, Phys. Rev. B 86
Original
2012
Cited alongside, same era.

Then

M. Barkeshli, C.-M. Jian, and X.-L. Qi, Phys. Rev. B 87
Original
2013
Later among the works it cites.
I. S. Eliëns, J. C. Romers, and F. A. Bais, Phys. Rev. B 90
Original
2014
Later among the works it cites.
B. Paredes, (2014), arXiv:1402.3567
Original
2014
Later among the works it cites.
M. B. Sahinoglu, D. Williamson, N. Bultinck, M. Marien, J. Haegeman, N. Schuch, and F. Verstraete, (2014), arXiv:1409.2150
Original
2014
Later among the works it cites.
N. Bultinck, M. Mariën, D. J. Williamson, M. B. Şahinoğlu, J. Haegeman, and F. Verstraete, (2015), arXiv:1511.08090
Original

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N. Schuch, D. Poilblanc, J. I. Cirac, and D. Pérez-García, Phys. Rev. B 86

Original

2012

Cited alongside, same era.

C. Fernández-González, N. Schuch, M. M. Wolf, J. I. Cirac, and D. Pérez-García, Phys. Rev. Lett. 109

Original

2012

Cited alongside, same era.

A. Kitaev and L. Kong, Commun. Math. Phys. 313

Original

2012

Cited alongside, same era.

N. Schuch, D. Poilblanc, J. I. Cirac, and D. Perez-Garcia, Phys. Rev. Lett. 111

Original

2013

Cited alongside, same era.

K. Duivenvoorden, M. Iqbal, J. Haegeman, F. Verstraete, and N. Schuch, in preparation

Cited in the paper.

Note that the converse is not true: There can be tensors of the form Eq. ( 1

Cited in the paper.

Note that the largest eigenvalue of the transfer operator for the normalization ⟨ ψ 4 a | ψ 4 a ⟩ \delimiter 69632778\psi_{4a}\delimiter 2532108\psi_{4a}\delimiter 86414091 of the non-abelian anyon 4 a 4a is degenerate, which allows it to have non-zero overlap with more than one sector (while without such a degeneracy, i.e., for abelian anyons, the normalized overlap must always be zero or one)

Cited in the paper.

2015

Later among the works it cites.

J. Haegeman, V. Zauner, N. Schuch, and F. Verstraete, Nature Comm. 6

Original

2015

Later among the works it cites.

C. Repellin, T. Neupert, B. A. Bernevig, and N. Regnault, Phys. Rev. B 92

Original

2015

Later among the works it cites.

C. Fernandez-Gonzalez, N. Schuch, M. M. Wolf, J. I. Cirac, and D. Perez-Garcia, Commun. Math. Phys. 333

Original

2015

Later among the works it cites.

T. Neupert, H. He, C. von Keyserlingk, G. Sierra, and B. A. Bernevig, Phys. Rev. B 93

Original

2016

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