In this paper we study a three-dimensional (3D) lattice spin model of ${\mathrm{CP}}^1$ Schwinger-bosons coupled with dynamical compact U(1) gauge bosons. The model contains two parameters; the gauge coupling and the hopping parameter of ${\mathrm{CP}}^1$ bosons. At large (weak) gauge couplings, the model reduces to the classical O(3) [O(4)] spin model with long-range and/or multispin interactions. It is also closely related to the recently proposed “Ginzburg-Landau” theory for quantum phase transitions of $s=1∕2$ quantum spin systems on a 2D square lattice at zero temperature. We numerically study the phase structure of the model by calculating specific heat, spin correlations, instanton density, and gauge-boson mass. The model has two phases separated by a critical line of second-order phase transition: O(3) spin-ordered phase and spin-disordered phase. The spin-ordered phase is the Higgs phase of U(1) gauge dynamics, whereas the disordered phase is the confinement phase. We find a crossover in the confinement phase which separates dense and dilute regions of instantons. On the critical line, spin excitations are gapless, but the gauge-boson mass is nonvanishing. This indicates that a confinement phase is realized on the critical line. To confirm this point, we also study the noncompact version of the model. A possible realization of a deconfinement phase on the criticality is discussed for the ${\mathrm{CP}}^N+\mathrm{U}\left(1\right)$ model with larger $N$.

• Received 11 April 2005

DOI:https://doi.org/10.1103/PhysRevB.72.075112