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We give a classification of gapped quantum phases of one-dimensional systems in the framework of matrix product states (MPS) and their associated parent Hamiltonians, for systems with unique as well as degenerate ground states and in both the ab[...]texto impreso
Fernández González, Carlos ; Mong, R. S. K. ; Pérez García, David ; Schuch, Norbert | American Physical Society | 2016Symmetrization of topologically ordered wave functions is a powerful method for constructing new topological models. Here we study wave functions obtained by symmetrizing quantum double models of a group G in the projected entangled pair states [...]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
Haegeman, Jutho ; Pérez García, David ; Cirac, Ignacio ; Schuch, Norbert | American Physical Society | 2012-08-03We introduce an order parameter for symmetry-protected phases in one dimension which allows us to directly identify those phases. The order parameter consists of stringlike operators and swaps, but differs from conventional string order operator[...]texto impreso
Schuch, Norbert ; Pérez García, David ; Cirac, Ignacio | 2010We introduce a framework for characterizing Matrix Product States (MPS) and Projected Entangled Pair States (PEPS) in terms of symmetries. This allows us to understand how PEPS appear as ground states of local Hamiltonians with finitely degenera[...]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
Schuch, Norbert ; Poilblanc, Didier ; Cirac, Juan I. ; Pérez García, David | American Physical Society | 2012-09We study resonating valence bond (RVB) states in the projected entangled pair states (PEPS) formalism. Based on symmetries in the PEPS description, we establish relations between the toric code state, the orthogonal dimer state, and the SU(2) si[...]texto impreso
Cirac, J. Ignacio ; Michalakis, Spyridon ; Pérez García, David ; Schuch, Norbert | American Physical Society | 2013-09-06We analyze a criterion which guarantees that the ground states of certain many-body systems are stable under perturbations. Specifically, we consider PEPS, which are believed to provide an efficient description, based on local tensors, for the l[...]texto impreso
Poilblanc, Didier ; Schuch, Norbert ; Pérez García, David ; Cirac, J. Ignacio | American Physical Society | 2012-07-06We examine in details the connections between topological and entanglement properties of short-range resonating valence bond (RVB) wave functions using projected entangled pair states (PEPS) on kagome and square lattices on (quasi)infinite cylin[...]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[...]
