Benchmark study of Nagaoka ferromagnetism by spin-adapted full configuration interaction quantum Monte Carlo

We investigate Nagaoka ferromagnetism in the two-dimensional Hubbard model with one hole using the spin-adapted [SU(2) conserving] full configuration interaction quantum Monte Carlo method. This methodology gives us access to the ground-state energies of all possible spin states S of finite Hubbard lattices, here obtained for lattices up to 26 sites for various interaction strengths (U). The critical interaction strength, Uc, at which the Nagaoka transition occurs is determined for each lattice and is found to be proportional to the lattice size for the larger lattices. Below Uc, the overall ground states are found to favour the minimal total spin (S = 12), and no intermediate spin state is found to be the overall ground state on lattices larger than 16 sites. However, at Uc, the energies of all the spin states are found to be nearly degenerate, implying that large fluctuations in total spin can be expected in the vicinity of the Nagaoka transition.