Abstract
We investigate a model of interacting Dirac fermions in 2 + 1 dimensions with M flavors and N colors having the U(M)×SU(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)×U(k) with k ∈ {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)×U(1)2, and U(5)→U(2)2×U(1) exist. For a large flavor-singlet mass, the increase of the chemical potential μ brings about M consecutive first-order transitions that separate the low-μ phase diagram with vanishing fermion density from the high-μ region with a high fermion density.
Highlights
Hadron physics, the Nambu-Jona-Lasinio (NJL) model [5, 6] is famous as a phenomenological effective theory of QCD [7, 8]
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)×U(k) with k ∈ {0, 1, 2, · · ·, M }, bearing a close resemblance to the vacuum structure of three-dimensional QCD
We study thermodynamics and symmetry breaking of an unconventional interacting model of Dirac fermions in 2 + 1 dimensions at finite temperature and chemical potential in the large-N limit, where N denotes the number of “colors.” Each fermion comes in M different flavors
Summary
We consider a system of two-component Dirac fermions ψsiα in 2 + 1 dimensions. Here α = 1, 2 are spinor indices, i = 1, · · · , N are color indices and s = 1, · · · , M are flavor indices. The four-fermion interactions of the form (2.1) arise in the random matrix model proposed in [50] which gives the sign of the interaction terms. We underline that these signs are essential for the results of the present work. Assuming that the condition g22 > M g12 is fulfilled, the integral over the φ field can be carried out and leads to the result. According to the Coleman-Mermin-Wagner-Hohenberg theorem, in the absence of long range interactions, continuous symmetries cannot be broken spontaneously in twodimensions which includes 2+1 dimensions at nonzero temperature. We always analyze the large N limit, but in appendix C we argue that even at finite N the same phase transitions still may be observed in particular if they are of first order
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