Towards the phase diagram of fermions coupled with $SO(3)$ quantum links in (2 + 1)−D

Quantum link models (QLMs) are generalizations of Wilson’s lattice gauge theory formulated with finite-dimensional link Hilbert spaces. In certain cases, the non-Abelian Gauss Law constraint can be exactly solved, and the gauge invariant subspace embedded onto local spin Hamiltonians for efficient quantum simulation. In (1 + 1)D previous studies of the SO(3) QLM coupled to adjoint fermionic matter have been shown to reflect key properties of QCD and nuclear physics, including distinct confining/deconfining phases and hadronic bound states. We extend the model to (2 + 1)D dimensions for the first time, and report on our initial results. We review the construction of gauge-invariant state space for the proposed models, and study the single-plaquette ground state via exact-diagonalisation. We provide indications of a rich phase diagram which shows both spontaneous and explicit chiral symmetry breaking, confinement, and distinct magnetic phases characterised by different plaquette expectation values.