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.

arXiv comment44 pages. v2: references added

References in corpus (51)

• The electronic properties of graphene
• Topological Insulators in Three Dimensions
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Exact evolution equation for the effective potential
• QCD Phenomenology based on a Chiral Effective Lagrangian
• Color superconductivity in dense quark matter
• NJL-model analysis of dense quark matter
• Dirac materials
• Dirac Semimetals in Two Dimensions
• Dirac Fermions in Solids - from High Tc cuprates and Graphene to Topological Insulators and Weyl Semimetals
• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• The Rare Two-Dimensional Materials with Dirac Cones
• Discovery of Weyl fermion semimetals and topological Fermi arc states
• Spectral Density of the QCD Dirac Operator near Zero Virtuality
• Random Matrix Theory and Chiral Symmetry in QCD
• Inhomogeneous chiral condensates
• Inhomogeneous Condensates in the Thermodynamics of the Chiral NJL_2 model
• Four - Fermi Theories in Fewer Than Four Dimensions
• From relativistic quantum fields to condensed matter and back again: Updating the Gross-Neveu phase diagram
• Asymptotic safety: a simple example
• A Twisted Kink Crystal in the Chiral Gross-Neveu model
• Dirac-Weyl fermions with arbitrary spin in two-dimensional optical superlattices
• Phase transition and critical behaviour of the d=3 Gross-Neveu model
• Phases Of Adjoint QCD${}_3$ And Dualities
• Random matrix theory and $QC{D}_3$
• A Symmetry Breaking Scenario for QCD${}_3$
• Quantum critical behavior in three dimensional lattice Gross-Neveu models
• Phonons, pions and quasi-long-range order in spatially modulated chiral condensates
• Emergence of Tricritical Point and Liquid-Gas Phase in the Massless 2+1 Dimensional Gross-Neveu Model
• Origin of fermion masses without spontaneous symmetry breaking
• Coulomb interaction effect in tilted Weyl fermion in two dimensions
• Critical Flavor Number in the Three Dimensional Thirring Model
• The Three Dimensional Thirring Model for Small N_f
• Large-N analysis of (2+1)-dimensional Thirring model
• Collective modes and Kosterlitz-Thouless transition in a magnetic field in the planar Nambu--Jona-Lasino model
• Mass generation without phase coherence in the Chiral Gross-Neveu Model at finite temperature and small N in 2+1 dimensions
• Phase diagram of the large $N$ Gross-Neveu model in a finite periodic box
• Many-flavor Phase Diagram of the (2+1)d Gross-Neveu Model at Finite Temperature
• Strongly Interacting Two-Dimensional Dirac Fermions
• Phases of QCD${}_3$ from Non-SUSY Seiberg Duality and Brane Dynamics
• Metastable Vacua in Large-$N$ QCD${}_3$
• Towards Critical Physics in 2+1d with U(2N)-Invariant Fermions
• Low-Temperature Properties of Two-Dimensional Ideal Ferromagnets
• Scale-invariance and scale-breaking in parity-invariant three-dimensional QCD
• The 2+1 Dimensional NJL Model at Finite Temperature
• Chiral phase transition in a planar four-Fermi model in a tilted magnetic field
• Superconducting phase transitions induced by chemical potential in (2+1)-dimensional four-fermion quantum field theory
• Charting the phase diagram of QCD${}_3$
• The next to leading order effective potential in the 2+1 dimensional Nambu-Jona-Lasinio model at finite temperature
• Phases of $\mathbf{U}({\mathbf{N}}_{\mathbf{c}})$ QCD${}_3$ from Type 0 Strings and Seiberg Duality
• Random matrix approach to three-dimensional QCD with a Chern-Simons term

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