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Hidden Grassmann Structure in the XXZ Model II: Creation Operators

Herman E. Boos, M. Jimbo, T. Miwa +2 more

arXiv:0801.1176Communications in Mathematical PhysicsSep 15, 2008133 citations

Hidden Grassmann Structure in the XXZ Model IV: CFT Limit

H. Boos, M. Jimbo, T. Miwa +1 more

arXiv:0911.3731Communications in Mathematical PhysicsApr 21, 201065 citations

Grassmann Variables

Mark S. Swanson

Elsevier eBooksJan 1, 19920 citations

Hidden Grassmann structure in the XXZ model III: Introducing Matsubara direction

M. Jimbo, T. Miwa, Fedor Aleksandrovich Smirnov

We address the problem of computing temperature correlation functions of the XXZ chain, within the approach developed in our previous works. In this paper we calculate the expected values of a fermionic basis of quasi-local operators, in the infinite volume limit while keeping the Matsubara (or Trotter) direction finite. The result is expressed in terms of two basic quantities: a ratio $ρ(\z)$ of transfer matrix eigenvalues, and a nearest neighbour correlator $ω(\z,ξ)$. We explain that the latter is interpreted as the canonical second kind differential in the theory of deformed Abelian integrals.We address the problem of computing temperature correlation functions of the XXZ chain, within the approach developed in our previous works. In this paper we calculate the expected values of a fermionic basis of quasi-local operators, in the infinite volume limit while keeping the Matsubara (or Trotter) direction finite. The result is expressed in terms of two basic quantities: a ratio $ρ(\z)$ of transfer matrix eigenvalues, and a nearest neighbour correlator $ω(\z,ξ)$. We explain that the latter is interpreted as the canonical second kind differential in the theory of deformed Abelian integrals.

Aug 16, 201694 citations

Long-range order in the frustrated XXZ model

秀稔西森, Hidetoshi Nishimori

Sep 1, 19920 citations

6 HIDDEN GRASSMANN STRUCTURE IN THE XXZ MODEL

H. Boos, M. Jimbo, T. Miwa +2 more

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

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