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

We investigate the finite-density phase diagram of a non-abelianSU(2)lattice gauge theory in(1+1)-dimensions using tensor network methods. We numerically characterise the phase diagram as a function of the matter filling and of the matter-field coupling, identifying different phases, some of them appearing only at finite densities. For weak matter-field coupling we find a meson BCS liquid phase, which is confirmed by second-order analytical perturbation theory. At unit filling and for strong coupling, the system undergoes a phase transition to a charge density wave of single-site (spin-0) mesons via spontaneous chiral symmetry breaking. At finite densities, the chiral symmetry is restored almost everywhere, and the meson BCS liquid becomes a simple liquid at strong couplings, with the exception of filling two-thirds, where a charge density wave of mesons spreading over neighbouring sites appears. Finally, we identify two tri-critical points between the chiral and the two liquid phases which are compatible with aSU(2)2Wess-Zumino-Novikov-Witten model. Here we do not perform the continuum limit but we explicitly address the globalU(1)charge conservation symmetry.