Thermodynamic Bethe ansatz equation from fusion hierarchy of osp(1|2) integrable spin chain

TL;DR

This paper derives thermodynamic Bethe ansatz equations for an osp(1|2) integrable spin chain using the quantum transfer matrix method, providing a comprehensive analysis of finite-temperature properties.

Contribution

It introduces the fusion hierarchy of the QTM for osp(1|2) and derives the associated T- and Y-systems, leading to integral equations for thermodynamic quantities.

Findings

Derived TBA equations matching previous results based on the string hypothesis

Established functional relations (T- and Y-systems) for the osp(1|2) spin chain

Provided a framework for analyzing finite-temperature properties of the model

Abstract

The thermodynamic Bethe ansatz (TBA) and the excited state TBA equations for an integrable spin chain related to the Lie superalgebra osp(1|2) are proposed by the quantum transfer matrix (QTM) method. We introduce the fusion hierarchy of the QTM and derive the functional relations among them (T-system) and their certain combinations (Y-system). Their analytical property leads to the non-linear integral equations which describe the free energy and the correlation length at any finite temperatures. With regard to the free energy, they coincide with the TBA equation (math-ph/9911010, Mod. Phys. Lett. A, 14, 2427 (1999)) based on the string hypothesis.