T-system and thermodynamic Bethe ansatz equations for solvable lattice models associated with superalgebras

TL;DR

This paper develops the T-system and thermodynamic Bethe ansatz equations for solvable lattice models linked to the superalgebra osp(1|2s), providing new eigenvalue formulas, duality relations, and connecting TBA to the string hypothesis.

Contribution

It introduces a novel T-system and TBA equations for models associated with osp(1|2s), including eigenvalue formulas and duality relations, advancing understanding of superalgebra-based integrable models.

Findings

Eigenvalue formula of transfer matrix in dressed vacuum form

Discovery of duality among DVFs

Derivation of TBA equations matching the string hypothesis

Abstract

An analytic Bethe ansatz is carried out related to the Lie superalgebra osp(1|2s). We present an eigenvalue formula of a transfer matrix in dressed vacuum form (DVF) labeled by a Young (super) diagram. Remarkable duality among DVFs is found. A complete set of transfer matrix functional relations (T-system) is proposed as a reduction of a Hirota-Miwa equation. We also derive a thermodynamic Bethe ansatz (TBA) equation from this T-system and the quantum transfer matrix method. This TBA equation is identical to the one from the string hypothesis.