The natural integrable correlated strongly coupled boson system in 1 + 1 dimensions is the $q$-boson hopping model; we calculate its critical exponent $\theta$ and determine its correlation functions. For small couplings the $q$-boson model has natural connections with the Bose gas and the $\mathrm{XY}$ models of very large spin for which $\theta \text{'}\mathrm{s}$ and correlators are reported. For large couplings the hopping model is a new phase of interacting bosons substantially different from the impenetrable Bose gas.

• Received 22 February 1994

DOI:https://doi.org/10.1103/PhysRevLett.72.3933