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).

Jun 30, 200679 citations

Hidden Grassmannian Structure in the XXZ Model

Tetsuji Miwa

This review is based on the joint work by Herman Boos, Michio Jimbo, Fedor Smirnov, Yishihiro Takeyama and T. M. We present an exponential formula for the correlation functions of the XXZ model. The formula is given in terms of a kind of monodromy operators in the sense of the quantum inverse scattering method. The opertors satisfy anti-commutation relations, and acting on the space of quasi-local operators as annihilation operators. Construction of creation operators is also given.

Progress of Theoretical Physics SupplementJan 1, 20090 citations