Hidden Grassmann structure in the XXZ model

Abstract

For the critical XXZ model, we consider the space W of operators which are products of local operators with a disorder operator. We introduce two anti-commutative family of operators b(z), c(z) which act on the space W. 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 W can be expressed in terms of an exponential of a quadratic form of b(z), c(z).

20 pages, no figure, minor misprints corrected

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• Traces on the Sklyanin algebra and correlation functions of the eight-vertex model
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• Density matrix of a finite sub-chain of the Heisenberg anti-ferromagnet

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