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We show that two different tensors defining the same translational invariant injective projected entangled pair state (PEPS) in a square lattice must be the same up to a trivial gauge freedom. This allows us to characterize the existence of any [...]texto impreso
Fernández González, C. ; Schuch, N. ; Wolf, M.M. ; Cirac, J.I. ; Pérez García, David | Springer | 2015-01For every Matrix Product State (MPS) one can always construct a so-called parent Hamiltonian. This is a local, frustration free, Hamiltonian which has the MPS as ground state and is gapped. Whenever that parent Hamiltonian has a degenerate groun[...]texto impreso
De las Cuevas, G. ; Cubitt, J.L. ; Wolf, M.M. ; Pérez García, David | American Institute of Physics Inc. | 2016We show a fundamental limitation in the description of quantum many-body mixed states with tensor networks in purification form. Namely, we show that there exist mixed states which can be represented as a translationally invariant (TI) matrix pr[...]texto impreso
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 condit[...]texto impreso
Bañuls, M.C. ; Pérez García, David ; Wolf, M.M. ; Verstraete, F. ; Cirac, J.I. | American Physical Society | 2008Matrix product states can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system [Schon et al., Phys. Rev. Lett. 95, 110503 (2005)]. We introduce a family of states that extends this definition [...]texto impreso
Pérez García, David ; Wolf, M.M. ; Sanz, M. ; Verstraete, F. ; Cirac, J.I. | The American Physical Society | 2008-04-25We show that the existence of string order in a given quantum state is intimately related to the presence of a local symmetry by proving that both concepts are equivalent within the framework of finitely correlated states. Once this connection i[...]
