String order and symmetries in quantum spin lattices

2008/02/04 by David Pérez-Garcı́a, D. Perez-Garcia, M. M. Wolf +5 · 1 voice · 26 citations
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum many-body systems #cond-mat.stat-mech #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevlett.100.167202

published as Phys. Rev. Lett. 100, 167202 (2008) · 5 pages, 1 figure

arxiv created 2008/02/04 · openalex publication_date 2008/04/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 to understand in a straightforward way many of the properties of string order parameters, like their robustness/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.

Citations

• Fault-tolerant quantum computation by anyons
• Two soluble models of an antiferromagnetic chain

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Discussions

• I am reading the paper String order and symmetries in quantum spin lattices by D. Pérez-García, M. M. Wolf, M. Sanz, F. Verstraete, and J. I. Cirac, Phys. Rev. Lett. 100 , 167202 (2008) , specifically [stackexchange, 2 points]

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