Improved honeycomb and hyperhoneycomb lattice Hamiltonians for quantum simulations of non-Abelian gauge theories

Improved Kogut-Susskind Hamiltonians for quantum simulations of non-Abelian Yang-Mills gauge theories are developed for honeycomb (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>2</a:mn><a:mo>+</a:mo><a:mn>1</a:mn><a:mi mathvariant="normal">D</a:mi></a:mrow></a:math>) and hyperhoneycomb (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mrow><d:mn>3</d:mn><d:mo>+</d:mo><d:mn>1</d:mn><d:mi mathvariant="normal">D</d:mi></d:mrow></d:math>) spatial tessellations. This is motivated by the desire to identify lattices for quantum simulations that involve only 3-link vertices among the gauge field group spaces in order to reduce the complexity in applications of the plaquette operator. For the honeycomb lattice, we derive a classically <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi mathvariant="script">O</g:mi><g:mo stretchy="false">(</g:mo><g:msup><g:mi>b</g:mi><g:mn>2</g:mn></g:msup><g:mo stretchy="false">)</g:mo></g:math>-improved Hamiltonian, with <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>b</l:mi></l:math> being the lattice spacing. Tadpole improvement via the mean-field value of the plaquette operator is used to provide the corresponding quantum improvements. We have identified the (nonchiral) hyperhoneycomb as a candidate spatial tessellation for <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mrow><n:mn>3</n:mn><n:mo>+</n:mo><n:mn>1</n:mn><n:mi mathvariant="normal">D</n:mi></n:mrow></n:math> quantum simulations of gauge theories, and determined the associated <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi mathvariant="script">O</q:mi><q:mo stretchy="false">(</q:mo><q:mi>b</q:mi><q:mo stretchy="false">)</q:mo></q:math>-improved Hamiltonian.