Ground-State Long-Range Order of the Two-Dimensional Quantum Antiferromagnet

Abstract

The two-dimensional quantum antiferromagnet is of active current interest. One of the main unsettled problems is whether magnetic long-range order exists or not in the ground state of the quantum antiferromagnet on the square lattice. In the present contribution we treat the XYZ model, $$H = \mathop \Sigma \limits_{\alpha \in \Lambda } \Sigma \left( {{J_x}S_\alpha ^xS_{\alpha + \delta }^x + {J_y}S_\alpha ^yS_{\alpha + \delta }^y + {J_z}S_\alpha ^zS_{\alpha + \delta }^z} \right),\left( {{J_x},{J_y},{J_z}\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ >} } 0} \right)$$ (1) and derive the parameter region in which long-range order certainly exists. We also show that long-range order along the non-principal axis (e.g. z-axis in the XY-like region) exists in the XXZ model (J x =J y =1, J z =Δ)under certain conditions.KeywordsThermodynamic LimitParameter RegionHexagonal LatticePresent ContributionSpin ComponentThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.