Spin Exchange-Enabled Quantum Simulator for Large-Scale Non-Abelian Gauge Theories

A central requirement for the faithful implementation of large-scale lattice gauge theories (LGTs) on quantum simulators is the protection of the underlying gauge symmetry. Recent advancements in the experimental realizations of large-scale LGTs have been impressive, albeit mostly restricted to Abelian gauge groups. Guided by this requirement for gauge protection, we propose an experimentally feasible approach to implement large-scale non-Abelian <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mi>SU</a:mi><a:mo stretchy="false">(</a:mo><a:mi>N</a:mi><a:mo stretchy="false">)</a:mo></a:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><f:mrow><f:mi mathvariant="normal">U</f:mi></f:mrow><f:mo stretchy="false">(</f:mo><f:mi>N</f:mi><f:mo stretchy="false">)</f:mo></f:math> LGTs with dynamical matter in <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><l:mi>d</l:mi><l:mo>+</l:mo><l:mn>1</l:mn><l:mrow><l:mrow><l:mi mathvariant="normal">D</l:mi></l:mrow></l:mrow></l:math>, enabled by two-body spin-exchange interactions realizing local emergent gauge-symmetry stabilizer terms. We present two concrete proposals for <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><p:mn>2</p:mn><p:mo>+</p:mo><p:mn>1</p:mn><p:mrow><p:mrow><p:mi mathvariant="normal">D</p:mi></p:mrow></p:mrow><p:mspace width="0.2em"/><p:mi>SU</p:mi><p:mo stretchy="false">(</p:mo><p:mn>2</p:mn><p:mo stretchy="false">)</p:mo></p:math> and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><w:mrow><w:mi mathvariant="normal">U</w:mi></w:mrow><w:mo stretchy="false">(</w:mo><w:mn>2</w:mn><w:mo stretchy="false">)</w:mo></w:math> LGTs, including dynamical bosonic matter and induced plaquette terms, that can be readily implemented in current ultracold-molecule and next-generation ultracold-atom platforms. We provide numerical benchmarks showcasing experimentally accessible dynamics, and demonstrate the stability of the underlying non-Abelian gauge invariance. We develop a method to obtain the effective gauge-invariant model featuring the relevant magnetic plaquette and minimal gauge-matter coupling terms. Our approach paves the way towards near-term realizations of large-scale non-Abelian quantum link models in analog quantum simulators.