Nagaoka Ferromagnetism in finite-size arrays: Connectivity and Magnetic Perturbations effects

Motivated by the first experimental demonstration of Nagaoka Ferromagnetism (NFM) [1] and recent theoretical work [2,4], we study the inter-dot connectivity conditions and external perturbations (external magnetic fields and spin-orbit coupling) affecting NFM in finite-size arrays. Employing exact diagonalization of the Hubbard Hamiltonian, we determine the ratio of the local interaction U to the characteristic hopping integral t, U/t, at which NFM occurs. In agreement with Tasaki [4], we find that NFM appears if the array is 1) biconnected (i.e., the array remains connected after removing one site), and 2) formed by elemental loops that go through four sites. We find the U/t ratio increases quadratically with the connectivity in square arrays, and that other bipartite arrays can also exhibit NFM. We focus on the role of the magnetic field, as there are regimes where it can destroy the ferromagnetic state [1]. We analyze how spin correlations depend on system parameters to describe their effect on the resulting ground state. Our results suggest alternative geometries for experimental testing of NFM.

[1] J. P. Dehollain, et al., Nature 579, 528 (2020).

[2] D. Buterakos and S. Das Sarma, Phys. Rev. B 100, 224421 (2019).

[3] Y. Li, K. Liu, and G. W. Bryant, arXiv:2404.03889.

[4] H. Tasaki (2020). Physics and mathematics of quantum many-body systems (Vol. 66). Berlin: Springer.