Computational scheme for the spin-$\frac{1}{2}$ Heisenberg antiferromagnet based on an octapartite description of the square lattice

We introduce a parameterization of the Hilbert space of a spin-$\frac{1}{2}$ Heisenberg antiferromagnet using an octapartite description of the square lattice. This provides a systematic way to model the ground-state wave function within a truncated basis. To prove its effectiveness we study systems with up to 64 spins using exact diagonalization. At significantly reduced computational cost, we get ground-state energies within 1% of the best published values. Its noniterative nature and lack of exploitation of spatial symmetries make this approach suitable for generalization to doped systems and for integration into iterative procedures.

Figure 1

(Color online) Square lattice divided in octads (shaded areas). Sites positioned similarly inside octads have the same label. Each is surrounded by neighbors with different labels.

Figure 2

(Color online) (a) Overlap ${\left|⟨GS,C_s|GS,C_s+\frac{2}{N}⟩\right|}^2$ between ground-state wave functions corresponding to adjacent values of $C_s$ for $N=16$, 32, and 64. Note that for $N=64$, the overlap is already 95% for $C_s=\frac{1}{4}$; (b) Fractional change $\frac{1}{E_{GS}}\frac{d{E}_{GS}}{d{C}_s}$ in ground-state energy corresponding to different $C_s$ cutoffs. The lines are linear fits to the data.

Figure 3

(Color online) GS energy computed at specific $C_s$ values (symbols) and the extrapolation to $C_s=1$ (solid lines) for $N=16$, 32, and 64. The horizontal dashed lines are the lowest values from Ref. 15. Inset: expectation values of the noncommuting operators $\sqrt{⟨m^2⟩}$ and $⟨{\overline{S}}_r\cdot {\overline{S}}_{r+\left(L/2,L/2\right)}⟩$.