Fermions, strings, and gauge fields in lattice spin models

Details Fermions, strings, and gauge fields in lattice spin models Fermions, strings, and gauge fields in lattice spin models

2003-02-22

arxiv.org/abs/cond-mat/0302460v2

Phys.Rev. B67 (2003) 245316

Physics

Condensed Matter

Strongly Correlated Electrons

RevTeX4, 11 page. Homepage, see http://dao.mit.edu/~wen

Scientific paper

10.1103/PhysRevB.67.245316

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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