Dense QC2D2 with uniform matrix product states

A bstract We study cold dense single-flavor SU(2) gauge theory in (1 + 1) dimensions in the thermodynamic limit using a gauge-invariant variational uniform matrix product state ansatz. This formulation provides a first-principles approach to dense QCD. We show that, at finite baryon density, the infrared behavior is consistent with a Tomonaga–Luttinger liquid: the central charge is determined to be c = 1, and the two-point function of the baryon-number density exhibits spatial modulation with the wavenumber predicted by Tomonaga–Luttinger liquid theory. The Luttinger parameter varies smoothly from K ≃ 1 in the dilute-baryon regime to K ≃ 1/2 at higher densities, suggesting a quarkyonic crossover. Furthermore, the quark momentum distribution reveals the coexistence of a quark Fermi sea with a baryonic infrared description, thereby realizing the quarkyonic picture from first principles.