  Simulating fermions coupled to spin degrees of freedom, relevant for a range
of quantum field theories, represents a promising application for quantum
simulators. Mapping fermions to qubits is challenging in $2+1$ and higher
spacetime dimensions, and mapping bosons demands substantial
quantum-computational overhead. These features complicate the realization of
mixed fermion-boson quantum systems in digital quantum computers. We propose a
native fermion-(large-)spin analog quantum simulator by utilizing dopant arrays
in silicon. Specifically, we show how to use a dynamical lattice of coupled
nuclear spins and conduction-band electrons to realize a quantum field theory:
an extended Jackiw-Rebbi model involving coupled fermions and quantum rotors.
We demonstrate the feasibility of observing dynamical mass generation and a
confinement-deconfinement quantum phase transition in 1+1 dimensions on this
platform, even in the presence of strong long-range Coulomb interactions.
Furthermore, we employ finite-temperature Hartree-Fock-Bogoliubov simulations
to investigate the dynamics of mass generation in two-dimensional square and
honeycomb arrays, showing that this phenomenon can be simulated with realistic
experimental parameters. Our findings reveal two distinct phases, and
demonstrate robustness against the addition of Coulomb interactions. Finally,
we discuss experimental signatures of the phases through transport and local
charge sensing in dopant arrays. This study lays the foundation for quantum
simulations of quantum field theories exhibiting fermions coupled to spin
degrees of freedom using donors in silicon.
