Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field

We present a conjecture for the density matrix of a finite segment of the XXZ chain coupled to a heat bath and to a constant longitudinal magnetic field. It states that the inhomogeneous density matrix, conceived as a map which associates with every local operator its thermal expectation value, can be written as the trace of the exponential of an operator constructed from weighted traces of the elements of certain monodromy matrices related to $U_q (\hat{\mathfrak{sl}}_2)$ and only two transcendental functions pertaining to the one-point function and the neighbour correlators, respectively. Our conjecture implies that all static correlation functions of the XXZ chain are polynomials in these two functions and their derivatives with coefficients of purely algebraic origin.Comment: 35 page

Modified Tetrahedron Equations and Related 3D Integrable Models

Using a modified version of the tetrahedron equations we construct a new family of $N$-state three-dimensional integrable models with commuting two-layer transfer-matrices. We investigate a particular class of solutions to these equations and parameterize them in terms of elliptic functions. The corresponding models contain one free parameter $k$ -- an elliptic modulus.Comment: 26 pages, LaTeX fil

Asymptotic Behavior of the Emptiness Formation Probability in the Critical Phase of XXZ Spin Chain

We study the Emptiness Formation Probability (EFP) for the spin 1/2 XXZ spin chain. EFP P(n) detects a formation of ferromagnetic string of the length n in the ground state. It is expected that EFP decays in a Gaussian way for large strings P(n) ~ n^{-gamma} C^{-n^2}. Here, we propose the explicit expressions for the rate of Gaussian decay C as well as for the exponent gamma. In order to confirm the validity of our formulas, we employed an ab initio simulation technique of the density-matrix renormalization group to simulate XXZ spin chain of sufficient length. Furthermore, we performed Monte-Carlo integration of the Jimbo-Miwa multiple integral for P(n). Those numerical results for P(n) support our formulas fairly definitely.Comment: 9 pages, 2 figure

Single top quarks at the Fermilab Tevatron

We present a calculation of the single top quark cross section for proton-antiproton interactions with sqrt(s) = 1.8 TeV at the Fermilab Tevatron collider. We examine the effects of top mass, parton distribution functions, QCD scale, and collision energy, on each of the component production mechanisms, and study the kinematic distributions for standard model electroweak production. At the upgraded Tevatron with sqrt(s) = 2.0 TeV and high luminosity, it will be possible to test the nature of the Wtb coupling using single top production. We estimate the sensitivity to measure the single top cross section, and thus to directly measure V_tb and the top quark partial width. We show what happens to the V_tb measurement when an anomalous (V+A) component is added to the Wtb coupling, and how the top quark polarization affects the kinematic distributions.Comment: 31 pages including 11 figure

Hidden Grassmann Structure in the XXZ Model IV: CFT limit

The Grassmann structure of the critical XXZ spin chain is studied in the limit to conformal field theory. A new description of Virasoro Verma modules is proposed in terms of Zamolodchikov's integrals of motion and two families of fermionic creation operators. The exact relation to the usual Virasoro description is found up to level 6.Comment: 44 pages, 1 figure. Version 3: some corrections are don