Hidden Grassmann Structure in the XXZ Model

By H. Boos, Michio Jimbo, Tetsuji Miwa, F. Smirnov, Yoshihiro Takeyama. 2006

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For the critical XXZ model, we consider the space $$\mathcal{W}_{[\alpha]}$$ of operators which are products of local operators with a disorder operator. We introduce two anti-commutative families of operators $${\bf {b}}(\zeta), {\bf {c}}(\zeta)$$ which act on $$\mathcal{W}_{[\alpha]}$$. These operators are constructed as traces over representations of the q-oscillator algebra, in close analogy with Baxter’s Q-operators. We show that the vacuum expectation values of operators in $$\mathcal{W}_{[\alpha]}$$ can be expressed in terms of an exponential of a quadratic form of $${\bf {b}}(\zeta), {\bf {c}}(\zeta)$$.

Subfields: Algebra and Number Theory, Condensed Matter Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cae0f35091fa3ddcaea91f77304c808458021f49