2007/02/12 by H. Boos, M. Jimbo, Boos, H. +9 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #hep-th #math.QA
paper · pdf · doi:10.48550/arxiv.hep-th/0702086
34 pages, no figure
arxiv created 2007/02/12 · arxiv updated 2009/12/01
In the recent study of correlation functions for the infinite XXZ spin chain, a new pair of anti-commuting operators b(z), c(z) was introduced. They act on the space of quasi-local operators, which are local operators multiplied by the disorder operator. For the inhomogeneous chain with the spectral parameters ξk, these operators have simple poles at z2=ξk2. The residues are denoted by bk, ck. At q=i, we show that the operators bk, ck are cubic monomials in free fermions. In other words, the action of these operators is very simple in the fermion basis. We give an explicit construction of these fermions. Then, we show that the existence of the fermionic basis is a consequence of the Grassmann relation, the equivariance with respect to the action of the symmetric group and the reduction property, which are all valid for the operators bk, ck in the case of generic q.