Simulating Nagaoka Ferromagnetism in a 2×2 Quantum Dot Array

The Fermi-Hubbard model provides a description of interacting electrons in a lattice. The interaction between electrons in arrays of electrostatically defined quantum dots is naturally described by a Fermi-Hubbard Hamiltonian; moreover, the high-degree of tunability in these systems make them a perfect platform to explore different regimes of the Hubbard model through analogue quantum simulations¹.

Last year we established a 2x2 gate-defined quantum dot array as a promising solid-state analogue quantum simulator². Here we present results on simulation of Nagaoka Ferromagnetism in this system. We experimentally observe a ferromagnetic ground state in an almost-half-filled lattice, as predicted³. We use the high-levels of control in our system to manipulate the Hamiltonian parameters and perform measurements that test the validity of our observations. For example, breaking the periodic boundary condition gets rid of the ferromagnetic ground state altogether. To our knowledge, this is the first experimental verification of Nagaoka’s prediction as well as the first simulation of magnetism using quantum dot arrays.

[1] T. Hensgens, et. al., Nature 548, 70 (2017)
[2] U. Mukhopadhyay, et. al., Appl. Phys. Lett. 112, 183505 (2018)
[3] Y. Nagaoka, Phys. Rev. 147, 392-405 (1966)