Emergent phases of strongly-correlated fermions are of central interest in condensed matter physics. Quantum systems with engineered Hamiltonians can be used as quantum simulators of such many-body systems to provide insights beyond the capabilities of classical computers. Semiconductor gate-defined quantum-dot arrays, owing to their in-situ tunability and flexible geometry, is an ideal platform for simulating Fermi-Hubbard and Heisenberg models. In this talk, I will first briefly review the quantum simulation experiments of Mott metal-insulator transition [1] and Nagaoka ferromagnetism [2], which demonstrate the excellent control of interaction parameters in quantum-dot arrays. I will then introduce our recent work on simulating a Heisenberg spin chain [3]. In this experiment we developed several experimental techniques including many-body spin-state preparation, singlet-triplet correlation measurements, and characterization of the quantum system with energy spectroscopy and global coherent oscillations. We used these techniques to tune and probe a homogeneously coupled Heisenberg spin chain formed in a linear array of four single-electron quantum dots, and find good agreement between experiment and numerical simulation. Our demonstrated control and techniques combined with flexibility of the quantum dot lattice geometry design opens new opportunities to simulate quantum many-body systems, including spin liquid physics and quantum phase transitions.

[1] T. Hensgens, T. Fujita, L. Janssen, X. Li, C. J. van Diepen, C. Reichl, W. Wegscheider, S. Das Sarma, and L. M. K. Vandersypen, Quantum Simulation of a Fermi-Hubbard Model Using a Semiconductor Quantum Dot Array, Nature 548, 70 (2017)

[2] J. P. Dehollain, U. Mukhopadhyay, V. P. Michal, Y. Wang, B. Wunsch, C. Reichl, W. Wegscheider, M. S. Rudner, E. Demler, and L. M. K. Vandersypen, Nagaoka Ferromagnetism Observed in a Quantum Dot Plaquette, Nature 579, 528 (2020).

[3] C. J. van Diepen*, T.-K. Hsiao*, U. Mukhopadhyay, C. Reichl, W. Wegscheider, and L. M. K. Vandersypen, Quantum Simulation of Antiferromagnetic Heisenberg Chain with Gate-Defined Quantum Dots, Physical Review X 11, 041025 (2021)