Geometric phases and criticality in spin systems

A general formalism of the relation between geometric phases produced by circularly evolving interacting spin systems and their criticality behaviour is presented. This opens up the way for the use of geometric phases as a tool to probe regions of criticality without having to undergo a quantum phas...

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Published in:Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2006-12, Vol.364 (1849), p.3463-3476
Main Authors: Pachos, Jiannis K, Carollo, Angelo C.M
Format: Article
Language:English
Subjects:
Atoms
Berry Phases
Critical Phenomena
Critical points
Eigenvalues
Energy gaps
Expected values
General Physics
Geometric topology
Ground state
Magnetic fields
Mathematical vectors
Topology
XY model
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container_title Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences
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creator Pachos, Jiannis K
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description A general formalism of the relation between geometric phases produced by circularly evolving interacting spin systems and their criticality behaviour is presented. This opens up the way for the use of geometric phases as a tool to probe regions of criticality without having to undergo a quantum phase transition. As a concrete example, a spin-1/2 chain with XY interactions is considered and the corresponding geometric phases are analysed. Finally, a generalization of these results to the case of an arbitrary spin system is presented.
doi_str_mv 10.1098/rsta.2006.1894
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source JSTOR Archival Journals and Primary Sources Collection; Royal Society Publishing Jisc Collections Royal Society Journals Read & Publish Transitional Agreement 2025 (reading list)
subjects Atoms
Berry Phases
Critical Phenomena
Critical points
Eigenvalues
Energy gaps
Expected values
General Physics
Geometric topology
Ground state
Magnetic fields
Mathematical vectors
Topology
XY model
title Geometric phases and criticality in spin systems
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