Effect of anisotropy on the ground-state magnetic ordering of the spin-half quantum J1XXZ-J2XXZ model on the square lattice

We study the zero-temperature phase diagram of the two-dimensional quantum J(1)(XXZ)-J(2)(XXZ) spin-1/2 anisotropic Heisenberg model on the square lattice. In particular, the effects of the anisotropy Delta on the z-aligned Neel and (collinear) stripe states, as well as on the xy-planar-aligned Neel and collinear stripe states, are examined. All four of these quasiclassical states are chosen in turn as model states, on top of which we systematically include the quantum correlations using a coupled cluster method analysis carried out to very high orders. We find strong evidence for two quantum triple points (QTPs) at (Delta(c)=-0.10 +/- 0.15, J(2)(c)/J(1)=0.505 +/- 0.015) and (Delta(c)=2.05 +/- 0.15, J(2)(c)/J(1)=0.530 +/- 0.015), between which an intermediate magnetically disordered phase emerges to separate the quasiclassical Neel and stripe collinear phases. Above the upper QTP (A greater than or similar to 2.0) we find a direct first-order phase transition between the Neel and stripe phases, exactly. as for the classical case. The z-aligned and xy-planar-aligned phases meet precisely at Delta=1, also as for the classical case. For all values of the anisotropy parameter between those of the two QTPs there exists a narrow range of values of J(2)/J(1), alpha(c1)(Delta)<J(2)/J(1)<alpha(c2)(Delta), centered near the point of maximum classical frustration, J(2)/J(1)=1/2, for which the intermediate phase exists. This range is widest precisely at the isotropic point, Delta=1, where alpha(c1)(1)=0.44 +/- 0.01 and alpha(c2)(1)=0.59 +/- 0.01. The two QTPs are characterized by values Delta=Delta(c) at which alpha(c1)(Delta(c))=alpha(c2)(Delta(c)).