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

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.

5 pages, 5 figures

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• Fermionic atoms in a 3D optical lattice: Observing Fermi-surfaces, dynamics and interactions
• Quantized acoustoelectric current in a finite-length ballistic quantum channel: The noise spectrum
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Cited by in corpus (17)

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• Environment-induced decay dynamics of anti-ferromagnetic order in Mott-Hubbard systems
• Deterministic preparation of supersinglets with collective spin projections
• Temperature dependent angular dispersions of surface acoustic waves on GaAs
• Anti-Newtonian dynamics and self-induced Bloch oscillations of correlated particles
• Correlation induced $d$-wave pairing in quantum dot square lattice
• Solid-state magnetic traps and lattices
• Simulating spin systems with Majorana networks
• Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution
• EPR pairing dynamics in Hubbard model with resonant $U$
• Trapping polar molecules by surface acoustic waves