arXiv:cond-mat/9911043 · Journal of Physics A Mathematical and General

Exactly solvable quantum spin ladders associated with the orthogonal and symplectic Lie algebras

Murray T. Batchelor, Jan de Gier, Jon Links, M. Maslen

Published Mar 23, 2000• 25 citations

Abstract

We extend the results of spin ladder models associated with the Lie algebras su (2 n ) to the case of the orthogonal and symplectic algebras o (2 n ), sp (2 n ) where n is the number of legs for the system. Two classes of models are found whose symmetry, either orthogonal or symplectic, has an explicit n dependence. Integrability of these models is shown for an arbitrary coupling of XX -type rung interactions and applied magnetic field term.

DOI: 10.1088/0305-4470/33/12/101

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arXiv:cond-mat/9911043 · Journal of Physics A Mathematical and General

Exactly solvable quantum spin ladders associated with the orthogonal and symplectic Lie algebras

Murray T. Batchelor, Jan de Gier, Jon Links, M. Maslen

Published Mar 23, 2000• 25 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/0305-4470/33/12/101

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We study boundary rung defects in n-leg quantum spin ladders with

\mathrm{SU}{(2}^{n})

leg symmetry. The rung interactions are parametrized by two coupling parameters J and ${J}^{\ensuremath{'}}$ interpolating between the uniform spin tube ${(J}^{\ensuremath{'}}=J)$ and the open spin ladder ${(J}^{\ensuremath{'}}=0).$ The rung defect at the edge of the ladder has rung coupling parameters

{J}_{d}

and ${J}_{d}^{\ensuremath{'}}.$ The conditions for the integrability of the model are investigated as a function of n, J, ${J}^{\ensuremath{'}},$

{J}_{d},

and ${J}_{d}^{\ensuremath{'}},$ and the Bethe Ansatz equations for the exact solution are derived. The boundary quantum critical behavior is discussed. The conditions for the formation of a local moment (boundary bound state due to the defect) are studied. In the absence of a magnetic field such a bound state is only possible for even-legged spin tubes, while for odd-legged ladders a bound state can only occur in a large magnetic field. Depending on the parameters of the host this local moment may be screened in analogy to the Kondo effect.