Anisotropy-Induced Ordering in the Quantum $J_1\mathrm{\text{−}}{J}_2$ Antiferromagnet

We study the effect of spin anisotropies on a frustrated quantum antiferromagnet using the $J_1\mathrm{\text{−}}{J}_2^{XXZ}$ model on the square lattice. The $T=0$ and finite-$T$ phase diagrams of this model are obtained utilizing spin-wave theory, exact diagonalization, and quantum Monte Carlo calculations. We find that anisotropic frustration tends to stabilize $XY$- and Ising-like ordered phases, while the disordered spin-liquid phase is restricted to a small region of the phase diagram. The ordered phases are separated by first-order transitions and exhibit a nontrivial reentrance phenomenon.

Figure 1

Zero-temperature phase diagram of the $S=1/2$ $J_1$-$J_2^{XXZ}$ model within linear spin-wave theory. Solid and dashed lines denote the second- and first-order transitions, respectively. Inset: nonmagnetic region magnified.

Figure 2

Phase diagram of the $S=1/2$ $J_1$-$J_2^Z$ model. Magnetic (and corresponding bosonic) phases are indicated. The horizontal dashed line marks the BKT critical temperature of the $S=1/2$ $XY$ model [11], and the dotted line is a logarithmic fit for small ${\alpha }_z$ (see text). Inset: zoom on the tricritical point.

Figure 3

Left panel: the double-peak structure in the histograms of the collinear magnetization $m_{\mathrm{c}\mathrm{o}\mathrm{l}\mathrm{l}}$ for system size $L=32$ and temperature $T/J_1=0.36$. Right panel: Binder's fourth cumulant of the collinear magnetization and the CCL order parameter for ${\alpha }_z=1.3$.

Figure 4

Zero-temperature phase diagram of the $J_1$-$J_2^{XXZ}$ model from exact diagonalization on clusters of size $N$.

Figure 5

Global phase diagram of the $J_1$-$J_2^{XXZ}$ model. The leftmost filled area represents the region with broken rotational symmetry in lattice space but unbroken symmetry in spin space; data for the CCL transition are from Ref. 6.