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Physica Scripta

On a long range variant of the discrete NLS equation and algebraic Bethe ansatz

A. Ghose Choudhury, Asesh Roy Chowdhury

Published Feb 1, 1996• 8 citations
Publisher

Abstract

We have constructed a new Quantum Nonlinear Schrödinger type periodic chain in which the interaction is long-range and not the usual nearest neighbour one. Using a new form of the transfer matrix with inhomogeneities at the lattice sites a long range Hamiltonian and its eigenvalues are extracted by using the algebraic Bethe ansatz.
DOI
10.1088/0031-8949/53/2/001

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Quantum spin chains arise naturally from perturbative large- N field theories and matrix models. The Hamiltonian of such a model is a long-range deformation of nearest-neighbour type interactions. Here, we study the most general long-range integrable spin chain with spins transforming in the fundamental representation of . We derive the Hamiltonian and the corresponding asymptotic Bethe ansatz at the leading four perturbative orders with several free parameters. Furthermore, we propose Bethe equations for all orders and identify the moduli of the integrable system. We finally apply our results to plane-wave matrix theory and show that the Hamiltonian in a closed sector is not of this form and therefore not integrable beyond the first perturbative order. This also implies that the complete model is not integrable.
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