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Nuclear Physics B

Exact bethe ansatz for a quantum nonlinear schrödinger model with the most general supermatrices

Yu‐Kui Zhou

Published Nov 1, 1989• 2 citations
Publisher
DOI
10.1016/0550-3213(89)90555-5

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A lattice version of the quantum nonlinear Schrodinger (NLS) equation is considered, which has a significant simple form and fulfils most of the criteria desirable for such lattice variants of field models. Unlike most of the known lattice NLS equations, the present model belongs to a class which does not exhibit the usual symmetry properties. However, this lack of symmetry itself seems to be responsible for the remarkable simplification of the relevant objects in the theory, such as the Lax operator, the Hamiltonian and other commuting conserved quantities as well as their spectra. The model allows exact quantum solution through the algebraic Bethe ansatz and also a straightforward and natural generalization to the vector case, thus giving a new exact lattice version of the vector NLS model. A deformation representing a new quantum integrable system involving Tamm-Dancoff-like q-boson operators is constructed.