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arXiv:cond-mat/0306025 · Journal of Physics A Mathematical and General

Exactly soluble isotropic spin-½ ladder models

Vladimir Gritsev, D. Baeriswyl

Published Nov 26, 2003• 8 citations
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Abstract

The undeformed limit of the dilute two-colour braid–monoid algebra gives a natural basis for the description of spin-½ ladder models, and allows different Baxterization ansätze. Based on this observation we find the complete classification of exactly soluble generalized isotropic spin-½ ladder models.
DOI
10.1088/0305-4470/36/49/001

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A detailed study of an S = ½ 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.
Two integrable quantum spin ladder systems will be introduced associated with the fundamental su (2|2) solution of the Yang-Baxter equation. The first model is a generalized quantum Ising system with Ising rung interactions. In the second model the addition of extra interactions allows us to impose Heisenberg rung interactions without violating integrability. The existence of a Bethe ansatz solution for both models allows us to investigate the elementary excitations for antiferromagnetic rung couplings. We find that the first model does not show a gap whilst in the second case there is a gap for all positive values of the rung coupling.