Jordan-Wigner transformations and their generalizations for multidimensional systems
Abstract
In the paper nonlinear transformations of the Jordan-Wigner (JW) type are introduced in the form different from the ones known previously, for the purpose of expressing multi-index Pauli operators in terms of multi-index Fermi creation and annihilation operators. These JW transformations in the general case being a subject of a rather complicated algebra of transposition relations between various sets of Fermi creation and annihilation operators, depending on the common multiindex of the latter, is shown. As an example, the two- and three- dimensional transformations of the JW type are investigated, their properties and possible applications in analysis of a couple of lattice models of statistical mechanics and also an example of application of these transformations to problems of self-avoiding walks in graph theory, are discussed. The relation of the obtained transformations to the previously known transformations of the JW type for higher dimensions is shown.
Cite
@article{arxiv.cond-mat/9807388,
title = {Jordan-Wigner transformations and their generalizations for multidimensional systems},
author = {Martin S. Kochman'ski},
journal= {arXiv preprint arXiv:cond-mat/9807388},
year = {2007}
}
Comments
22 pages, REVTEX