Z3 lattice gauge theory as a toy model for dense QCD

We propose the (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>3</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:math>)-dimensional <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi mathvariant="double-struck">Z</c:mi><c:mn>3</c:mn></c:msub></c:math> lattice gauge theory coupled with the 2-flavor Wilson-Dirac fermion as a toy model for studying quantum chromodynamics (QCD) at nonzero density. We study its phase diagram in the space of the lattice gauge couplings <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msup><f:mi>g</f:mi><f:mn>2</f:mn></f:msup></f:math> and the quark chemical potentials <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>μ</h:mi></h:math> and discuss the similarity and difference compared with anticipated behaviors of actual QCD. This model also provides a testing ground for various algorithms of the numerical Hamiltonian formalism as its Hilbert space is finite-dimensional in a finite box. Published by the American Physical Society 2024