PEPS as unique ground states of local Hamiltonians

David Pérez-Garcia, Frank Verstraete, J. Ignacio Cirac, Michael M. Wolf

Publications: Contribution to journalArticlePeer Reviewed


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.
Original languageEnglish
Pages (from-to)650-663
Number of pages14
JournalQuantum Information & Computation
Issue number6-7
Publication statusPublished - Jul 2008

Austrian Fields of Science 2012

  • 103025 Quantum mechanics


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