Exact solution of a<i>q</i>-boson hopping model

Abstract

Quantum-group deformation of ordinary bosons yields the q bosons or nonlinear phonons. We solve exactly, for any real q&gt;1, including q=\ensuremath{\infty}, a one-dimensional q-boson lattice ``hopping model,'' and calculate asymptotically its correlation functions. The model is a nonlinear model of strongly interacting ordinary bosons. Our solution solves the equivalent quantum difference differential nonlinear Schr\"odinger model. Approximation reduces this to a nonintegrable boson Hubbard-type model with q bosons as fundamental particles. One special limit q\ensuremath{\rightarrow}\ensuremath{\infty} of the hopping model is the classical $XY--- chain.