Quantum simulator for the Hubbard model with long-range Coulomb interactions using surface acoustic waves

TL;DR

This paper proposes a practical quantum simulation scheme for the Hubbard model with long-range Coulomb interactions using surface acoustic waves in a GaAs/AlGaAs heterojunction, enabling experimental exploration of quantum phase transitions.

Contribution

It introduces a novel experimental setup employing surface acoustic waves to realize a Hubbard model with long-range interactions in a 2D electron gas.

Findings

Numerical estimates suggest experimental feasibility of observing quantum phase transitions.

The scheme allows probing metallic and insulating states via conductance and noise.

Potential to experimentally study strongly correlated electron phenomena.

Abstract

A practical experimental scheme for a quantum simulator of strongly correlated electrons is proposed. Our scheme employs electrons confined in a two dimensional electron gas in a GaAs/AlGaAs heterojunction. Two surface acoustic waves are then induced in the GaAs substrate, which create a two dimensional ``egg-carton'' potential. The dynamics of the electrons in this potential is described by a Hubbard model with long-range Coulomb interactions. The state of the electrons in this system can be probed via its conductance and noise properties. This allows the identification of a metallic or insulating state. Numerical estimates for the parameters appearing in the effective Hubbard model are calculated using the proposed experimental system. These calculations suggest that observations of quantum phase transition phenomena of the electrons in the potential array are within experimental reach.