2013
DOI: 10.1103/physrevb.88.115108
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Robustness in projected entangled pair states

Abstract: We 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 low energy physics arising from local interactions. In order to assess stability in the framework of PEPS, one thus needs to understand how physically allowed perturbations of the local tensor affect the properties of the global state. In this paper, we show that a restr… Show more

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Cited by 24 publications
(34 citation statements)
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“…More generally one could add an arbitrary perturbation that lies within the MPO-injectivity subspace (this can be constructed by applying the MPO projector to an arbitrary perturbation) to the MPO-isometric PEPS tensor to find a new MPOinjective PEPS that will generically have a finite correlation length. For a sufficiently small symmetric perturbation the resulting MPO-injective PEPS will lie in the same phase of matter as the fixed-point MPO-isometric PEPS [13,62].…”
Section: Perturbations Away From Fixed-pointsmentioning
confidence: 97%
“…More generally one could add an arbitrary perturbation that lies within the MPO-injectivity subspace (this can be constructed by applying the MPO projector to an arbitrary perturbation) to the MPO-isometric PEPS tensor to find a new MPOinjective PEPS that will generically have a finite correlation length. For a sufficiently small symmetric perturbation the resulting MPO-injective PEPS will lie in the same phase of matter as the fixed-point MPO-isometric PEPS [13,62].…”
Section: Perturbations Away From Fixed-pointsmentioning
confidence: 97%
“…The following results have been developed in a sequence of works [25][26][27] on the definition and stability of topologically ordered systems (see also related work on stability of tensor network states [28,34]). It is not our intention to provide a complete discussion of topological order, and we will we will simply paraphrase the relevant definitions and results here.…”
Section: Topological Ordermentioning
confidence: 99%
“…Its canonical form has facilitated the distinction between injective and non-injective MPS [3], (which determines the ground state degeneracy of the parent Hamiltonian, and is linked to many other physical properties, see e.g. [4][5][6]), which has led to the classification of gapped phases of one-dimensional systems [7]. This mathematical understanding has allowed to characterize global properties of the state, such as topological order or symmetries, in a local way [8,9].…”
Section: Introductionmentioning
confidence: 99%