Antiferromagnetism in two-dimensional $t\text{−}J$ model: A pseudospin representation

We discuss a pseudospin representation of the two-dimensional $t\text{−}J$ model. We introduce pseudospins associated with empty sites, deriving a representation of the $t\text{−}J$ model that consists of local spins and spinless fermions. We show, within a mean-field approximation, that our representation of $t\text{−}J$ model corresponds to the isotropic antiferromagnetic Heisenberg model in an effective magnetic field. The strength and the direction of the effective field are determined by the hole doping $\delta$ and the orientation of pseudospins associated with empty sites, respectively. We find that the staggered magnetization in the standard representation corresponds to the component of magnetization perpendicular to the effective field in our pseudospin representation. Using a many-body Green’s function method, we show that the staggered magnetization decreases with increasing hole doping $\delta$ and disappears at $\delta \approx 0.06–0.12$ for $t∕J=2.5–5$. Our results are in good agreement with experiments and numerical calculations in contradistinction to usual mean-field methods.

Figure 1

Bloch sphere describing the orientation of pseudospins.

Figure 2

Components of magnetization $m^x$ and $m^z$ as a function of $B^z$ at different temperatures $T$ for $D^x∕\overline{J}=0.01$ (solid lines) and $D^x∕\overline{J}=0$ (dotted lines).

Figure 3

(a) Particle-hole order parameter $\varphi$ as a function of doping $\delta$ at $T=0$ (independent of $t∕J$). (b) Staggered magnetization $M$ as a function of doping $\delta$ at $T=0$ for $t∕J=2.5$, $t∕J=3$, and $t∕J=5$.