Néel-Dimer Transition in Antiferromagnetic Heisenberg Model and Deconfinement of Spinons at the Critical Point

Details Néel-Dimer Transition in Antiferromagnetic Heisenberg Model and Deconfinement of Spinons at the Critical Point Néel-Dimer Transition in Antiferromagnetic Heisenberg Model and Deconfinement of Spinons at the Critical Point

2004-04-19

arxiv.org/abs/cond-mat/0404427v4

Phys. Rev. B70 174407(2004)

Physics

Condensed Matter

Strongly Correlated Electrons

Scientific paper

10.1103/PhysRevB.70.174407

Quantum phase transition from the N\'eel to the dimer states in an antiferromagnetic(AF) Heisenberg model on square lattice is studied. We introduce a control parameter $\alpha$ for the exchange coupling which connects the N\'eel ($\alpha=0$) and the dimer ($\alpha=1$) states. We employ the $CP^1$ (the Schwinger boson) representation of the $s={1\over 2}$ spin operator and integrate out the half of the $CP^1$ variables at odd sites and we obtain a $CP^1$ nonlinear $\sigma$ model. The effective coupling constant is a function of $\alpha$ and at $\alpha=0$ the $CP^1$ model is in the ordered phase which corresponds to the N\'eel 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 N\'eel state, the dynamical composite U(1) gauge field in the $CP^1$ model is in a Higgs phase and low-energy excitations are gapless spin wave. In the dimer phase, a confinement phase of the gauge theory is realized and low-energy excitations are $s=1$ magnons. For the critical point, we argue that a deconfinement phase, which is similar to the Coulomb phase in 3 spatial dimensions, is realized and $s={1\over 2}$ spinons appear as low-energy excitations.

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