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PEPS as unique ground states of local Hamiltonians · Around

2007

PEPS as unique ground states of local Hamiltonians

Perez-Garcia, David, Verstraete, Frank, Cirac, J. Ignacio et al.

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In this paper we consider projected entangled pair states (PEPS) on arbitrary lattices.

We construct local parent Hamiltonians for each PEPS and isolate a condition under which the state is the unique ground state of the Hamiltonian.
This condition, verified by generic PEPS and examples like the AKLT model, is an injective relation between the boundary and the bulk of any local region.
While it implies the existence of an energy gap in the 1D case we will show that in certain cases (e.g., on a 2D hexagonal lattice) the parent Hamiltonian can be gapless with a critical ground state.

Built on

V. Privman, M. Fisher, Phys. Rev. B 30
1950
Earlier work this paper cites.
I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki, Commun. Math. Phys. 115
1988
Earlier work this paper cites.
M. Fannes, B. Nachtergaele and R. F. Werner, Commun. Math. Phys. 144
1992
Earlier work this paper cites.
A. Klümper, A. Schadschneider, J. Zittartz, J. Phys. A 24
1992
Earlier work this paper cites.
H. Niggemann, A. Klümper, J. Zittartz, Eur. Phys. J. B 13
1997
Earlier work this paper cites.
J. R. Norris, Markov Chains
1997
Earlier work this paper cites.

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