Spinons in magnetic chains of arbitrary spins at finite temperatures

Abstract

The thermodynamics of solvable isotropic chains with arbitrary spins is addressed by the recently developed quantum transfer matrix (QTM) approach. The set of nonlinear equations which exactly characterize the free energy is derived by respecting the physical excitations at T = 0, spinons and RSOS kinks. We argue the implication of the present formulation to spinon character formula of level k = 2S SU(2) WZWN

The finite size spectrum of the 2-dimensional nonlinear σ-model

“…For large ℓ this equation is equivalent to the Bethe-Yang equations 19) if y 0 (θ) = e −ℓcoshθ y 1 (θ).This relation is consistent with the Y-system equations (1.3)…”

“…It is a common experience in the theory of Bethe Ansatz equations that the polynomials T k have only real roots inside the physical strip |Im θ| < q (see, for example, [19]). We denote the set of real roots of T k (which may be empty) by t k for k = 1, 2, .…”

Персистентные Токи В Открытых Спиновых Цепочках

“…Кроме того, остаются технические сложности, затрудняющие численное решение НИУ, в особенности при больших значениях ch φ. Эти сложности могут быть пре-одолены с помощью подбора точного обрезания бесконечной иерархии уравнений, похожего на обрезание для sl(2)-модели [21]. К тому же случай 0 < ch φ < 1, отве-чающий эрмитовым граничным членам в гамильтониане (1), не описывается пред-ставленным подходом.…”

Finite volume spectrum of superminimal models perturbed by

“…We also introduce the odd primitives of the kernel functions (see appendix D. for the choice of branch cuts of χ K (θ)), 10) that are important in writing the source terms containing information on the excitations: 13) where the second determination of any function: f II (θ) is defined as in [6] …”

“…It would be nice to extend Dunning's conjecture to excited states as well. To achieve this one has to start from higher spin vertex models and along the lines of [11] and extend the method described in [10] for excited states. Having the NLIEs for the excited states two applications can be of importance: the quantum group restriction leading to SU(2)-coset theories [31] perturbed by Φ (1) 13 and the large spin limit where this series should make contact with the N = 2 supersymmetric sine-Gordon model, whose finite size effects are of principal importance in the formulation of superstrings propagating in pp-wave background [32].…”