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Fermions, strings, and gauge fields in lattice spin models

Michael Levin·Xiao-Gang Wen
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Abstract

We investigate the general properties of lattice spin models with emerging fermionic excitations. We argue that fermions always come in pairs and their creation operator always has a string-like structure with the newly created particles appearing at the endpoints of the string. The physical implication of this structure is that the fermions always couple to a nontrivial gauge field. We present exactly soluble examples of this phenomenon in 2 and 3 dimensions. Our analysis is based on an algebraic formula that relates the statistics of a lattice particle to the properties of its hopping operators. This approach has the advantage that it works in any number of dimensions - unlike the flux-binding picture developed in FQH theory.

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Michael Levin, Xiao-Gang Wen. 2003-08-06. Fermions, strings, and gauge fields in lattice spin models. https://doi.org/10.1103/physrevb.67.245316

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