Realizing multi-orbital Emery models with ultracold atoms

TL;DR

This paper proposes an optical superlattice setup to realize the three-band Emery model with ultracold atoms, enabling controlled study of multi-orbital Hubbard physics relevant to cuprate superconductors.

Contribution

It introduces a novel optical lattice architecture for simulating the Emery model, including methods for benchmarking and extracting effective models from experiments.

Findings

Benchmarking with quantum walks confirms the tight-binding model.

Quantum Monte Carlo reveals a finite-temperature metal-insulator crossover.

Hamiltonian learning enables inference of effective single-band models.

Abstract

Strongly-correlated electrons in transition-metal oxides give rise to intriguing emergent phenomena, including high-temperature superconductivity in cuprates. While simplified one-band Hubbard models capture some aspects, explicitly describing the interplay of copper and oxygen orbitals -- as in the three-band Emery model -- is essential to capture the full phenomenology of cuprates. Quantum simulators based on ultracold atoms offer a promising route to study such systems in a controlled setting, but realizing realistic multi-orbital Hubbard models remains challenging. Here we propose an optical superlattice architecture that implements the three-band Emery model with ultracold fermions. By combining lattice beams with controllable interference, we engineer orbital degrees of freedom that reproduce key features of the cuprate band structure, while enabling independent control of orbital-dependent interactions and charge-transfer energy. We show that single-particle quantum walks can benchmark the resulting tight-binding model. Using determinant quantum Monte Carlo, we further investigate thermodynamic properties in the undoped regime and find a finite-temperature metal-insulator crossover accompanied by the onset of antiferromagnetic correlations accessible in current experiments. Finally, we apply a Hamiltonian learning protocol enabling to infer effective single-band Hubbard models from experimental realizations of Emery models. Our results provide a practical pathway to simulate multi-orbital Hubbard physics with quantum gas microscopes.