Abstract
Nonperturbative exact solutions are allowed for quantum integrable models in one space-dimension. Going beyond this class we propose an alternative Lax matrix approach, exploiting the hidden multi-space–time concept in integrable systems and construct a novel nonlinear Schrödinger quantum field model in quasi-two dimensions. An intriguing field commutator is discovered, confirming the integrability of the model and yielding its exact Bethe ansatz solution with rich scattering and bound-state properties. The universality of the scheme is expected to cover diverse models, opening up a new direction in the field.
Highlights
Introduction and MotivationA large number of quantum models in one space-dimension (1D) admits exact nonperturbative solutions, in spite of their nonlinear interaction
For a breakthrough, we look for new ideas and observe, that the rational ancestor Lax matrix depends on the spectral parameter λ only linearly, while its q-deformation depends on its trigonometric functions [3, 24]
quantum integrable (QI) models are associated with a discretized quantum Lax matrix U j(λ), the operator elements of which, for ensuring the integrability of the model, must satisfy certain algebraic relations, which are expressed in a compact matrix form through the quantum Yang-Baxter equation (QYBE)
Summary
A large number of quantum models in one space-dimension (1D) admits exact nonperturbative solutions, in spite of their nonlinear interaction This exclusive class of models, which includes field models, constitute the family of quantum integrable (QI) systems [1, 2, 3, 4, 5] with extraordinary properties, like association with a quantum Lax and a quantum R matrix, possessing rich underlying algebraic structures to satisfy the quantum Yang-Baxter equation (QYBE), existence of a commuting set of conserved operators with an exact solution of their eigenvalue problem (EVP), etc. The bound states, corresponding to a complex solution for the particle momentum, are found to exhibit unusual properties with a variable stability region, dependent on the particle number, coupling constant and the average particle momentum
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