Lattice gauge magnets: Local isospin from spin

Peter Orland; Daniel Rohrlich

doi:10.1016/0550-3213(90)90646-U

Lattice gauge magnets: Local isospin from spin

Peter Orland, Daniel Rohrlich

Research output: Contribution to journal › Article › peer-review

126 Scopus citations

Abstract

We study lattice hamiltonians with continuous local SU(2) gauge invariance, for which the Hilbert space on each link is finite dimensional. As these are gauge-invariant generalizations of quantum magnets, we call them lattice gauge magnets. The generators of gauge transformations are built out of local spin operators. In the simplest version of such a theory, the gauge field components belong to a representation of the algebra SO(5). Long-wavelength excitations of this model are gapless and nonrelativistic at the tree level. In 2 + 1 dimensions, we study a parity violating model, which we argue is equivalent to the topologically massive Yang-Mills theory.

Original language	English
Pages (from-to)	647-672
Number of pages	26
Journal	Nuclear Physics B
Volume	338
Issue number	3
DOIs	https://doi.org/10.1016/0550-3213(90)90646-U
State	Published - 16 Jul 1990
Externally published	Yes

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1016/0550-3213(90)90646-U

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AB - We study lattice hamiltonians with continuous local SU(2) gauge invariance, for which the Hilbert space on each link is finite dimensional. As these are gauge-invariant generalizations of quantum magnets, we call them lattice gauge magnets. The generators of gauge transformations are built out of local spin operators. In the simplest version of such a theory, the gauge field components belong to a representation of the algebra SO(5). Long-wavelength excitations of this model are gapless and nonrelativistic at the tree level. In 2 + 1 dimensions, we study a parity violating model, which we argue is equivalent to the topologically massive Yang-Mills theory.

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Lattice gauge magnets: Local isospin from spin

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