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

Daisuke Yoshioka·Gaku Arakawa·Ikuo Ichinose·Tetsuo Matsui
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Abstract

Quantum phase transition from the Néel to the dimer states in an antiferromagnetic(AF) Heisenberg model on square lattice is studied. We introduce a control parameter $α$ for the exchange coupling which connects the Néel ($α=0$) and the dimer ($α=1$) 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 $σ$ model. The effective coupling constant is a function of $α$ and at $α=0$ the $CP^1$ model is in the ordered phase which corresponds to the Néel state of the AF Heisenberg model. A phase transition to the dimer state occurs at a certain critical value of $α_C$ as $α$ increases. In the Néel 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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Daisuke Yoshioka, Gaku Arakawa, Ikuo Ichinose, Tetsuo Matsui. 2004-08-26. Néel-Dimer Transition in Antiferromagnetic Heisenberg Model and Deconfinement of Spinons at the Critical Point. https://doi.org/10.1103/physrevb.70.174407

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