Quantum Simulation of Dynamical Lattices using Electrons in Silicon Dopant Arrays

Analogue quantum simulation does not suffer from a sign problem and may provide an advantage for calculating the dynamics of lattice gauge theories (LGTs). However, quantum simulation of LGTs has largely been constrained to qubit systems which have a large overhead when mapping the fermions to spin-1/2 in higher dimensions. We propose to use dopant arrays in silicon to encode fermions in Si conduction band electrons. We additionally exploit the local nuclear spin of the dopants to simulate a quantum dynamical lattice. Specifically, we use the extended Fermi-Hubbard model to natively realize the rotor Jackiw-Rabbi model. In 1D, the latter allows the study of dynamical mass generation and confinement-deconfinement quantum phase transitions, while its phase diagram in 2D is less explored. We recover past results on 1D systems, even when accounting for the long-range Coulomb interactions present in dopant arrays. In addition, we map out the 2D phase diagram using Hartree-Fock simulations with realistic parameters. We discuss experimental signatures based on transport in dopant arrays. Our studies help pave the way toward practical quantum simulation of LGTs with donors in silicon.