Quantum simulation of Fermi-Hubbard models in semiconductor quantum-dot arrays

Abstract

We propose a device for studying the Fermi-Hubbard model with long-range Coulomb interactions using an array of coupled quantum dots defined in a semiconductor two-dimensional electron-gas system. Bands above the lowest energy band are used to form the Hubbard model, so that a high average electron density may be used to implement the device. We find that depending on the average electron density, the system is well described by a one- or two-band Hubbard model. Our device design enables the control of the ratio of the Coulomb interaction to the kinetic energy of the electrons independently to the filling of the quantum dots, such that a large portion of the Hubbard phase diagram may be probed. Estimates of the Hubbard parameters suggest that a metal-Mott insulator quantum phase transition and a $d$-wave superconducting phase should be observable using current technologies.