String order and symmetries in quantum spin lattices

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

Publications: Contribution to journalArticlePeer Reviewed

Abstract

We 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 is established, we provide a complete characterization of local symmetries in these states. The results allow us to understand in a straightforward way many of the properties of string order parameters, like their robustness or fragility under perturbations and their typical disappearance beyond strictly one-dimensional lattices. We propose and discuss an alternative definition, ideally suited for detecting phase transitions, and generalizations to two and more spatial dimensions.
Original languageEnglish
Article number167202
Number of pages4
JournalPhysical Review Letters
Volume100
Issue number16
DOIs
Publication statusPublished - 25 Apr 2008

Austrian Fields of Science 2012

  • 103025 Quantum mechanics

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