Berry phases, quantum phase transitions and Chern numbers

We study the relation between Chern numbers and quantum phase transitions (QPT) in the XY spin-chain model. By coupling the spin chain to a single spin, it is possible to study topological invariants associated to the coupling Hamiltonian. These invariants contain global information, in addition to...

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Bibliographic Details
Published in:Physica. B, Condensed matter Condensed matter, 2008-04, Vol.403 (5), p.1301-1302
Main Authors: Contreras, H.A., Reyes-Lega, A.F.
Format: Article
Language:English
Subjects:
Berry phases
Condensed matter: electronic structure, electrical, magnetic, and optical properties
Exact sciences and technology
General theory and models of magnetic ordering
Magnetic properties and materials
Physics
Quantum phase transitions
Spin chain models
Topological invariants
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Summary:We study the relation between Chern numbers and quantum phase transitions (QPT) in the XY spin-chain model. By coupling the spin chain to a single spin, it is possible to study topological invariants associated to the coupling Hamiltonian. These invariants contain global information, in addition to the usual one (obtained by integrating the Berry connection around a closed loop). We compute these invariants (Chern numbers) and discuss their relation to QPT. In particular we show that Chern numbers can be used to label regions corresponding to different phases.
ISSN:0921-4526
1873-2135
DOI:10.1016/j.physb.2007.10.131