An Exactly Solvable Model of Generalized Spin Ladder

TL;DR

This paper introduces an exactly solvable SU(2)-invariant spin ladder model, providing explicit solutions and a detailed phase diagram, advancing understanding of integrable quantum spin systems.

Contribution

The paper presents a new integrable spin ladder model with explicit R-matrix and L-operator, solved via Bethe ansatz, and derives its exact ground state phase diagram.

Findings

Model is integrable with infinite conserved quantities.

Explicit R-matrix and L-operator provided.

Exact ground state phase diagram derived.

Abstract

A detailed study of an $S={1\over2}$ spin ladder model is given. The ladder consists of plaquettes formed by nearest neighbor rungs with all possible SU(2)-invariant interactions. For properly chosen coupling constants, the model is shown to be integrable in the sense that the quantum Yang-Baxter equation holds and one has an infinite number of conserved quantities. The R-matrix and L-operator associated with the model Hamiltonian are given in a limiting case. It is shown that after a simple transformation, the model can be solved via a Bethe ansatz. The phase diagram of the ground state is exactly derived using the Bethe ansatz equation.