Ground state energy and mass gap of a generalised quantum spin ladder

TL;DR

This paper demonstrates that a specific quantum spin ladder Hamiltonian can be represented using the Hecke algebra, linking its spectrum to the well-studied XXZ chain, and derives thermodynamic properties from this connection.

Contribution

It introduces a new algebraic representation of a quantum spin ladder Hamiltonian, enabling the use of known XXZ chain results to analyze its spectrum and thermodynamic quantities.

Findings

Ground state energy derived from XXZ chain results

Mass gap calculated using the XXZ model at Δ = -5/3

Representation simplifies analysis of the quantum spin ladder

Abstract

We show that a 2-leg ladder hamiltonian introduced recently by Albeverio and Fei (cond-mat/9807341) can be made to satisfy the Hecke algebra. As a result we have found an equivalent representation of the eigenspectrum in terms of the spin-1/2 antiferromagnetic XXZ chain at $\Delta = - 5/3$. The values of thermodynamic quantities such as the ground state energy and mass gap follow from the known XXZ results.