Analog Quantum Simulator of a Quantum Field Theory with Fermion-Spin Systems in Silicon

TL;DR

This paper proposes a silicon-based analog quantum simulator for fermion-spin quantum field theories, demonstrating the feasibility of observing phase transitions and mass generation in 1+1 and 2D systems with realistic parameters.

Contribution

It introduces a native fermion-spin quantum simulator using dopant arrays in silicon, enabling simulation of complex quantum field theories with reduced overhead.

Findings

Feasibility of observing dynamical mass generation and phase transitions in 1+1 dimensions.

Simulation of mass generation phenomena in 2D arrays with realistic parameters.

Robustness of phase phenomena against Coulomb interactions.

Abstract

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.