Nagaoka Ferromagnetism Observed in a Quantum Dot Plaquette

Abstract

Engineered, highly-controllable quantum systems hold promise as simulators of emergent physics beyond the capabilities of classical computers [Feynman(1982)]. An important problem in many-body physics is itinerant magnetism, which originates purely from long-range interactions of free electrons and whose existence in real systems has been subject to debate for decades [Auerbach(1994), Mattis(2006)]. Here we use a quantum simulator consisting of a four-site square plaquette of quantum dots [Mukhopadhyay(2018)] to demonstrate Nagaoka ferromagnetism [Nagaoka(1966)]. This form of itinerant magnetism has been rigorously studied theoretically [Mattis(2003), Nielsen(2007), Oguri(2007), Stecher(2010)] but has remained unattainable in experiment. We load the plaquette with three electrons and demonstrate the predicted emergence of spontaneous ferromagnetic correlations through pairwise measurements of spin. We find the ferromagnetic ground state is remarkably robust to engineered disorder in the on-site potentials and can induce a transition to the low-spin state by changing the plaquette topology to an open chain. This demonstration of Nagaoka ferromagnetism highlights that quantum simulators can be used to study physical phenomena that have not yet been observed in any system before. The work also constitutes an important step towards large-scale quantum dot simulators of correlated electron systems.