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$\mathbb{Z}_3$ lattice gauge theory as a toy model for dense QCD

Published 11 Apr 2024 in hep-lat, hep-ph, and hep-th | (2404.07595v2)

Abstract: We propose the $(3+1)$-dimensional $\mathbb{Z}_3$ 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 $g2$ and the quark chemical potentials $\mu$ 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.

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