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The Fermi-Hubbard model describes the interaction between electrons in a lattice [1].
This seemingly simple model reveals strong quantum correlations which, on the one hand,
can explain striking phenomena such as superconductivity [2] and magnetism [3], but on
the other hand make solutions to the model quickly intractable by classical methods with
increasing lattice size.
The interaction between electrons in arrays of electrostatically defined quantum dots is
naturally described by a Fermi-Hubbard Hamiltonian. In the first half of the talk, I will
introduce these arrays and their basic experimental tool kits - individual control over electron
fillings in each dot, control over tunnel couplings between different pairs of dots, and readout
of electron spins [4]. These make the quantum dot arrays a powerful platform to explore
different regimes of the Hubbard model through analog quantum simulations.
The final half of the talk will be on a specific example of analog quantum simulation -
simulation of Nagaoka Ferromagnetism, which predicts a ferromagnetic ground state in an
almost-half-filled lattice [3,5]. The experiment was performed with 3 electrons in the 2x2 dot
array [6]. We used the high levels of control in our system to manipulate the Hamiltonian
parameters and achieve the ferromagnetic ground state. We also performed measurements
that test the validity of our interpretation. For example, breaking the periodic boundary con-
dition of the plaquette destroyed the signature of the ferromagnetic state. To our knowledge,
this is the first experimental verification of Nagaoka’s prediction after more than 50 years of
its introduction.
[1] J. Hubbard, P. Roy. Soc. Lon. A 276, 238-257 (1963).
[2] P. W. Anderson, J. Phys. Conf. Ser. 449, 012001 (2013).
[3] Y. Nagaoka, Phys. Rev. 147, 392-405 (1966).
[4] U. Mukhopadhyay, J.P. Dehollain, et. al., App. Phys. Lett. 112, 183505 (2018).
[5] D. C. Mattis, International Journal of Nanoscience 2, 165 (2003).
[6] J.P. Dehollain, U. Mukhopadhyay, et. al., Nature 579, 528-533 (2020). |