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, U₂, 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 U₂, 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 U₂, 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.