Analytic Bethe ansatz and functional relations related to tensor-like representations of type-II Lie superalgebrasB(r|s) andD(r|s)

Abstract

An analytic Bethe ansatz is carried out related to tensor-like representations of the type II Lie superalgebras B(r|s) = osp(2r + 1|2s)We present eigenvalue formulae of transfer matrices in dressed vacuum forms labeled by Young (super) diagrams. A class of transfer matrix functional relations (T -system) is discussed. In particular for B(0|s) = osp(1|2s) (s ∈ Z ≥1 ) case, a complete set of functional relations is proposed by using duality among dressed vacuum forms.

THERMODYNAMIC BETHE ANSATZ EQUATION FROM FUSION HIERARCHY OF osp(1|2) INTEGRABLE SPIN CHAIN

“…is same as that in [26]. Therefore the DVFs T e Note that this diagram corresponds to the Kac-Dynkin label 2m.…”

“…m (u, v) b and the functional relations among them by using the results for the rowto-row transfer matrix [26]. Although the quantity we want to evaluate is only T formulation.…”

“…g In this paper, we use the variable m in (3.10) slightly different from that in [26] for practical reason: the variable m in (3.10) corresponds to 2m in [26]. [26]:…”

Nonlinear integral equations for thermodynamics of thesl(r 1) Uimin Sutherland model

“…The high temperature expansion of the free energy is discussed, in which a solution of the T -system is given in terms of solutions of the Q-system. We expect that we can extend these results to other algebras by using the T -systems in [21,32,34,35,36,37,23].…”

“…One can also derive [13] Takahashi's NLIE from the T -system [20,21] of the QTM. In view of this fact, we have derived [22] NLIE with a finite number of unknown functions from our T -system [23] for the osp(1|2s) model for arbitrary rank s. In this paper, we shall further derive NLIE for the sl(r + 1) Uimin-Sutherland model [24,25] with only a finite number (the number of rank r) of unknown functions from the T -system [21]. This is the first explicit derivation of this type of NLIE for a vertex model associated with sl(r + 1) for arbitrary rank r…”