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We investigate the finite-density phase diagram of a non-abelian SU(2)lattice gauge theory in (1+1)-dimensions using tensor network methods. Wenumerically characterise the phase diagram as a function of the matter fillingand of the matter-field coupling, identifying different phases, some of themappearing only at finite densities. For weak matter-field coupling we find ameson BCS liquid phase, which is confirmed by second-order analyticalperturbation theory. At unit filling and for strong coupling, the systemundergoes a phase transition to a charge density wave of single-site (spin-0)mesons via spontaneous chiral symmetry breaking. At finite densities, thechiral symmetry is restored almost everywhere, and the meson BCS liquid becomesa simple liquid at strong couplings, with the exception of filling two-thirds,where a charge density wave of mesons spreading over neighbouring sitesappears. Finally, we identify two tri-critical points between the chiral andthe two liquid phases which are compatible with a $SU(2)_2$Wess-Zumino-Novikov-Witten model. Here we do not perform the continuum limitbut we explicitly address the global $U(1)$ charge conservation symmetry.

Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks