Cascade of phase transitions in a planar Dirac material

Abstract

We investigate a model of interacting Dirac fermions in $2+1$ dimensions with $M$ flavors and $N$ colors having the $\mathrm{U}(M)\times \mathrm{SU}(N)$ symmetry. In the large-$N$ limit, we find that the $\mathrm{U}(M)$ 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 $\mathrm{U}(M)\to \mathrm{U}(M-k)\times \mathrm{U}(k)$ with $k\in \{0,1,2,\cdots ,M\}$, 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 $\mathrm{U}(3)\to \mathrm{U}(1{)}^3$, $\mathrm{U}(4)\to \mathrm{U}(2)\times \mathrm{U}(1{)}^2$, and $\mathrm{U}(5)\to \mathrm{U}(2{)}^2\times \mathrm{U}(1)$ 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.

44 pages. v2: references added

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Cited by in corpus (3)

• Absence of inhomogeneous chiral phases in 2+1-dimensional four-fermion and Yukawa models
• Spontaneous non-Hermiticity in the (2+1)-dimensional Gross-Neveu model
• Spontaneous non-Hermiticity in the (2+1)-dimensional Thirring model