Quantum simulation of an antiferromagnetic Heisenberg chain with gate-defined quantum dots*

Emergent phases of strongly-correlated fermions are of central interest in condensed matter physics. Quantum systems with engineered Hamiltonians can be used as simulators of many-body systems to provide insights beyond the capabilities of classical computers. Magnetism naturally arises in the Mott-insulator regime of the Fermi-Hubbard model, where charges are localized and the spin degree of freedom remains. In this regime the occurrence of phenomena such as resonating valence bonds, frustrated magnetism, and spin liquids are predicted. Here we show that semiconductor quantum dots can be used to simulate quantum magnetism in the Mott-insulator regime. For this purpose we demonstrate several techniques including many-body spin-state preparation, singlet-triplet correlation measurements, and characterization of the quantum system with energy spectroscopy and global coherent oscillations. With these techniques we tune and probe a homogeneously coupled Heisenberg spin-chain in a linear array of four single-electron quantum dots, and find good agreement between experiment and numerical simulation. Our demonstrated control and techniques open new opportunities to simulate quantum magnetism, including spin liquid physics and quantum phase transitions.