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Benchmark study of Nagaoka ferromagnetism by spin-adapted full configuration interaction quantum Monte Carlo
Physical Review B  (IF4.036),  Pub Date : 2021-12-02, DOI: 10.1103/physrevb.104.235102
Sujun Yun, Werner Dobrautz, Hongjun Luo, Ali Alavi

We investigate Nagaoka ferromagnetism in the two-dimensional Hubbard model with one hole using the spin-adapted [$\text{SU}\left(2\right)$ 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, ${U}_{c}$, 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 ${U}_{c}$, the overall ground states are found to favour the minimal total spin ($S=\frac{1}{2}$), and no intermediate spin state is found to be the overall ground state on lattices larger than 16 sites. However, at ${U}_{c}$, 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.