Cascade of phase transitions in a planar Dirac material

We investigate a model of interacting Dirac fermions in 2 + 1 dimensions with M flavors and N colors having the U(M)xSU(N ) symmetry. In the large-N limit, we find that the U(M) symmetry is spontaneously broken in a variety of ways. In the vacuum, when the parity-breaking flavor-singlet mass is varied, the ground state undergoes a sequence of M first-order phase transitions, experiencing M + 1 phases characterized by symmetry breaking U(M)-> U(M - k)xU(k) with k is an element of {0, 1, 2, ... , M}, bearing a close resemblance to the vacuum structure of three-dimensional QCD. At finite temperature and chemical potential, a rich phase diagram with first and second-order phase transitions and tricritical points is observed. Also exotic phases with spontaneous symmetry breaking of the form as U(3)-> U(1)(3), U(4)-> U(2)xU(1)(2), and U(5)-> U(2)(2)xU(1) exist. For a large flavor-singlet mass, the increase of the chemical potential mu brings about M consecutive first-order transitions that separate the low-mu phase diagram with vanishing fermion density from the high-mu region with a high fermion density.