Journal
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
Volume 20, Issue 30-31, Pages 5239-5249Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0217979206036326
Keywords
intermediate symmetries; dimensional reduction; order out of disorder
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We discuss symmetries intermediate between global and local and formalize the notion of dimensional reduction adduced from such symmetries. We apply this generalization to several systems including liquid crystalline phases of Quantum Hall systems, transition metal orbital systems, frustrated spin systems, (p+ip) superconducting arrays, and sliding Luttinger liquids. By considering space-time reflection symmetries, we illustrate that several of these systems are dual to each other. In some systems exhibiting these symmetries, low temperature local orders emerge by an order out of disorder effect while in other systems, the dimensional reduction precludes standard orders yet allows for multiparticle orders (including those of a topological nature).
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