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String order and symmetries in quantum spin lattices.
D Pérez-García1, M M Wolf, M Sanz
1Departamento de Analisis Matematico, Universidad Complutense de Madrid, 28040 Madrid, Spain.
Physical Review Letters
|June 4, 2008
Summary
We demonstrate that string order in quantum states is equivalent to local symmetry in finitely correlated states. This finding simplifies understanding string order properties and enables new phase transition detection methods.
Area of Science:
- Quantum Information Theory
- Condensed Matter Physics
- Mathematical Physics
Background:
- String order parameters are crucial for characterizing complex quantum phases.
- Local symmetries play a key role in defining quantum states.
- Finitely correlated states provide a tractable framework for studying quantum many-body systems.
Purpose of the Study:
- To establish a direct equivalence between string order and local symmetry in finitely correlated states.
- To fully characterize local symmetries within this framework.
- To provide a new perspective on the properties and detection of quantum phases.
Main Methods:
- Equivalence proof between string order and local symmetry.
- Complete characterization of local symmetries in finitely correlated states.
- Analysis of string order parameter properties (robustness, dimensionality).
Main Results:
- String order and local symmetry are proven to be equivalent concepts in finitely correlated states.
- A comprehensive characterization of local symmetries is provided.
- Properties like robustness and dimensionality dependence of string order are explained.
Conclusions:
- The equivalence simplifies the understanding of string order parameters.
- The framework offers insights into phase transitions and generalizations to higher dimensions.
- This work provides a unified view of order and symmetry in quantum states.
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