Neel-dimer transition in an antiferromagnetic Heisenberg model and deconfinement of spinons at the critical point

Quantum phase transition from the Neel to the dimer states in an antiferromagnetic (AF) Heisenberg model on square lattice is studied. We introduce a control parameter a for the exchange coupling that connects the Neel (alpha=0) and the dimer (alpha=1) states. We employ the CP1 representation of the s=1/2 spin operator and integrate out the half of the CP1 variables at odd sites to obtain a CP1 nonlinear sigma model. The effective coupling constant is a function of alpha, and at alpha = 0, the CP1 model is in the ordered phase that corresponds to the Neel state of the AF Heisenberg model. A phase transition to the dimer state occurs at a certain critical value of alpha(C) as alpha increases. In the Neel state, the dynamical composite U(1) gauge field in the CP1 model is in a Higgs phase, and low-energy excitations are gapless spin waves. In the dimer phase, a confinement phase of the gauge theory with s=1 excitations is realized. For the critical point, we argue that a deconfinement phase, which is similar to the Coulomb phase in three spatial dimensions, is realized and s=1/2 spinons appear as low-energy excitations.