Dense quark matter forms a Luttinger liquid in two dimensions

Using a gauge-invariant matrix product state ansatz — essentially a one-dimensional quantum simulation free of the sign problem that plagues lattice QCD at finite density — the authors solve SU(2) gauge theory with matter in 1+1 dimensions across a range of baryon densities. The system consistently shows central charge c=1 and density correlations matching Tomonaga–Luttinger liquid theory, with the Luttinger parameter sliding from K≈1 at low density to K≈1/2 at higher density. Crucially, the quark momentum distribution reveals a quark Fermi sea coexisting with a baryonic low-energy description, providing a first-principles confirmation of the quarkyonic matter scenario proposed for real dense QCD.