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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
Cadarso, Andrea ; Sanz, Mikel ; Wolf, Michael M. ; Cirac, J.I. ; Pérez García, David | American Physical Society | 2013-01Based on the theory of Matrix Product States, we give precise statements and complete analytical proofs of the following claim: a large fractionalization in the magnetization or the need of long-range interactions imply large entanglement in the[...]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
Fernández González, Carlos ; Schuch, Norbert ; Wolf, Michael M. ; Cirac, J.I. ; Pérez García, David | American Physical Society | 2012-12We 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 li[...]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
Cuevas, Gemma de las ; Schuch, Norbert ; Pérez García, David ; Cirac, J.I. | IOP Publishing | 2013-12-10We analyze the description of quantum many-body mixed states using matrix product states and operators. We consider two such descriptions: (i) as a matrix product density operator of bond dimension D; and (ii) as a purification that is written a[...]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[...]texto impreso
Schuch, Norbert ; Poilblanc, Didier ; Cirac, J.I. ; Pérez García, David | American Physical Society | 2013We study the structure of topological phases and their boundaries in the projected entangled-pair states (PEPS) formalism. We show how topological order in a system can be identified from the structure of the PEPS transfer operator and subsequen[...]texto impreso
Lamata, C. ; Porras Torres, Diego ; Cirac, J.I. ; Goldman, J. ; Gabrielse, G. | American Physical Society | 2010-02Entanglement of isolated elementary particles other than photons has not yet been achieved. We show how building blocks demonstrated with one trapped electron might be used to make a model system and method for entangling two electrons. Applicat[...]
