PEPS as unique ground states of local Hamiltonians



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Pérez García, David and Verstraete, F. and Wolf, M.M. and Cirac, J.I. (2008) PEPS as unique ground states of local Hamiltonians. Quantum Information & Computation, 8 (6-7). pp. 650-663. ISSN 1533-7146

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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. To show this we invoke a mapping between classical and quantum models and prove that in these cases the injectivity relation between boundary and bulk solely depends on the lattice geometry.

Item Type:Article
Uncontrolled Keywords:Quantum computation; quantum cryptography
Subjects:Sciences > Physics > Quantum theory
ID Code:17822
Deposited On:21 Jan 2013 14:56
Last Modified:03 Dec 2014 16:02

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