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Gapless Hamiltonians for the toric code using the PEPS formalism · Around

2011

Gapless Hamiltonians for the toric code using the PEPS formalism

Fernández-González, Carlos, Schuch, Norbert, Wolf, Michael M. et al.

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We study Hamiltonians which have Kitaev's toric code as a ground state, and show how to construct a Hamiltonian which shares the ground space of the toric code, but which has gapless excitations with a continuous spectrum in the thermodynamic limit.

Our construction is based on the framework of Projected Entangled Pair States (PEPS), and can be applied to a large class of two-dimensional systems to obtain gapless "uncle Hamiltonians".

Built on

Commun. Math. Phys. 115
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M. A. Levin and X.-G. Wen, · 2005
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Cited in the paper.

Then

(2010), arXiv:1001.4363
Original
S. Bravyi and M. B. Hastings, · 2010
Later among the works it cites.
Phys. Rev. A 81
Original
C. V. Kraus, N. Schuch, F. Verstraete, and J. I. Cirac, · 2010
Later among the works it cites.
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N. Schuch, I. Cirac, and D. Pérez-García, · 2010
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Phys. Rev. B 82, 165119 (2010), arXiv:1003.1774
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X. Chen, B. Zeng, Z. C. Gu, I. Chuang, X. G. Wen, · 2010
Later among the works it cites.
(2011), arXiv:1109.1588
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S. Michalakis and J. Pytel, · 2011

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