Nested Cluster Algorithm for Frustrated Quantum Antiferromagnets

Frustrated antiferromagnets are important materials whose quantum Monte Carlo simulation suffers from a severe sign problem. We construct a nested cluster algorithm which uses a powerful strategy to address this problem. For the spin $\frac{1}{2}$ Heisenberg antiferromagnet on a kagome and on a frustrated square lattice the sign problem is eliminated for large systems. The method is applicable to general lattice geometries but limited to moderate temperatures.

Figure 1

Kagome lattice (left) and frustrated square (or anisotropic triangular) lattice (right) consisting of three sublattices $A$, $B$, $C$.

Figure 2

Probability distribution of $⟨\mathrm{Sign}{⟩}_i$ for the kagome lattice with $V=576$ spins and $\beta J=1$.

Figure 3

Volume-dependence of $⟨\mathrm{Sign}{⟩}_{+}$ and $⟨M_s^2\mathrm{Sign}{⟩}_{+}$ (rescaled by ${10}^{-6}$) for the kagome lattice with $\beta J=1$.

Figure 4

Coplanar staggered susceptibility ${\chi }_s$ and collinear Néel susceptibility ${\chi }_N$ as functions of the space-time volume $\beta V$ for the kagome as well as the frustrated ($J^{\prime }=J/4$) and unfrustrated ($J^{\prime }=0$) square lattice at fixed space/time aspect ratio $\sqrt{V}/\beta J=20$.