Cluster mean-field theory study of $J_1-J_2$ Heisenberg model on a square lattice

Abstract

We study the spin-1/2 $J_1$-$J_2$ Heisenberg model on a square lattice using the cluster mean-field theory. We find a rapid convergence of phase boundaries with increasing cluster size. By extrapolating the cluster size $L$ to infinity, we obtain accurate phase boundaries $J_2^{c1}\approx 0.42$ (between the N$\acute{e}$el antiferromagnetic phase and nonmagnetic phase), and $J_2^{c2}\approx 0.59$ (between nonmagnetic phase and the collinear antiferromagnetic phase). The transitions are identified unambiguously as second order at $J_2^{c1}$ and first order at $J_2^{c2}$. At finite temperature, we present a complete phase diagram with stable, meta-stable and unstable states near $J_2^{c2}$, being relevant to that of the anisotropic $J_1-J_2$ model. The uniform as well as staggered magnetic susceptibilities are also discussed.

15 pages, 8 figures, 1 table

References in corpus (1)

• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism

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