Observation of Nagaoka polarons in a Fermi-Hubbard quantum simulator.

Quantum interference can deeply alter the nature of many-body phases of matter. In the case of the Hubbard model, Nagaoka proved that introducing a single itinerant charge can transform a paramagnetic insulator into a ferromagnet through path interference. However, a microscopic observation of this kinetic magnetism induced by individually imaged dopants has been so far elusive.

Experimental realization of an extended Fermi-Hubbard model using a 2D lattice of dopant-based quantum dots.

The Hubbard model is an essential tool for understanding many-body physics in condensed matter systems. Artificial lattices of dopants in silicon are a promising method for the analog quantum simulation of extended Fermi-Hubbard Hamiltonians in the strong interaction regime. However, complex atom-based device fabrication requirements have meant emulating a tunable two-dimensional Fermi-Hubbard Hamiltonian in silicon has not been achieved.

Lanczos-boosted numerical linked-cluster expansion for quantum lattice models.

Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the limiting factor for these calculations. Here we show that a partial diagonalization of the largest clusters in the expansion using the Lanczos algorithm can be as useful as full diagonalization for the method while mitigating some of the time and memory issues.

Machine learning in electronic-quantum-matter imaging experiments.

For centuries, the scientific discovery process has been based on systematic human observation and analysis of natural phenomena. Today, however, automated instrumentation and large-scale data acquisition are generating datasets of such large volume and complexity as to defy conventional scientific methodology. Radically different scientific approaches are needed, and machine learning (ML) shows great promise for research fields such as materials science.

Spin transport in a Mott insulator of ultracold fermions.

Strongly correlated materials are expected to feature unconventional transport properties, such that charge, spin, and heat conduction are potentially independent probes of the dynamics. In contrast to charge transport, the measurement of spin transport in such materials is highly challenging. We observed spin conduction and diffusion in a system of ultracold fermionic atoms that realizes the half-filled Fermi-Hubbard model.