String Order and Symmetries in Quantum Spin Lattices

2008/04/22 by David Pérez-Garcı́a, M. M. Wolf, Mikel Sanz +2 · 1 voice · 5 citations
Physics and Astronomy · #Quantum many-body systems #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena

paper · pdf · doi:10.1103/physrevlett.100.167202

openalex publication_date 2008/04/22 · 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 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.

Citations

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

Cited by

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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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