Spin-liquid versus dimer phases in an anisotropic $J_1$-$J_2$ frustrated square antiferromagnet

The spin-1/2 $J_1$-$J_2$ antiferromagnet is a prototypical model for frustrated magnetism and one possible candidate for a realization of a spin-liquid phase. The generalization of this system on the anisotropic square lattice is given by the $J_1$-$J_2$-$J_1^{\prime }$-$J_2^{\prime }$ Heisenberg model, which can be treated by a renormalization group analysis of coupled frustrated chains. The $J_1$-$J_2$-$J_1^{\prime }$-$J_2^{\prime }$-model shows an interesting interplay of Néel order, dimerization, and spin-liquid behavior. Extrapolating the analytical findings supported by numerical results indicates that for the isotropic model the phase at intermediate coupling strength $0.4J_1\lesssim J_2\lesssim 0.6J_1$ is not a spin liquid, but has instead a staggered dimer order.

Figure 1

The generalized anisotropic $J_1$-$J_2$-$J_1^{\prime }$-$J_2^{\prime }$ antiferromagnet.

Figure 2

The phase diagram of the anisotropic $J_1$-$J_2$-$J_1^{\prime }$-$J_2^{\prime }$ model from the RG analysis as a function of the anisotropy $r$ and the frustration $f$. The analytical functions in Eqs. (7) and (10) are indistinguishable on this scale.

Figure 3

Numerical DMRG results for the phase diagram of two chains with in-chain frustration $f=J_2/J_1$ and interchain couplings $r=J_1^{\prime }/J_1=J_2^{\prime }/J_2$. Inset: Dimer order parameter (red solid line) and the derivative of the two-rung entropy (blue dashed line) as a function of $f$ for $J_1^{\prime }=J_1$ and $L=128$ rungs.