A frustrated quantum spin-${\boldmath s}$ model on the Union Jack lattice with spins ${\boldmath s>1/2}$

Abstract

The zero-temperature phase diagrams of a two-dimensional frustrated quantum antiferromagnetic system, namely the Union Jack model, are studied using the coupled cluster method (CCM) for the two cases when the lattice spins have spin quantum number $s=1$ and $s=3/2$. The system is defined on a square lattice and the spins interact via isotropic Heisenberg interactions such that all nearest-neighbour (NN) exchange bonds are present with identical strength $J_1>0$, and only half of the next-nearest-neighbour (NNN) exchange bonds are present with identical strength $J_2\equiv \kappa J_1>0$. The bonds are arranged such that on the $2\times 2$ unit cell they form the pattern of the Union Jack flag. Clearly, the NN bonds by themselves (viz., with $J_2=0$) produce an antiferromagnetic Néel-ordered phase, but as the relative strength $\kappa$ of the frustrating NNN bonds is increased a phase transition occurs in the classical case ($s\to \infty$) at ${\kappa }_c^{\mathrm{cl}}=0.5$ to a canted ferrimagnetic phase. In the quantum cases considered here we also find strong evidence for a corresponding phase transition between a Néel-ordered phase and a quantum canted ferrimagnetic phase at a critical coupling ${\kappa }_{c_1}=0.580\pm 0.015$ for $s=1$ and ${\kappa }_{c_1}=0.545\pm 0.015$ for $s=3/2$. In both cases the ground-state energy $E$ and its first derivative $dE/d\kappa$ seem continuous, thus providing a typical scenario of a second-order phase transition at $\kappa ={\kappa }_{c_1}$, although the order parameter for the transition (viz., the average ground-state on-site magnetization) does not go to zero there on either side of the transition.

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