$SO(8)$ unification and the large-N theory of superconductor-insulator transition of two-dimensional Dirac fermions

Abstract

Electrons on honeycomb or pi-flux lattices obey effective massless Dirac equation at low energies and at the neutrality point, and should suffer quantum phase transitions into various Mott insulators and superconductors at strong two-body interactions. We show that 35 out of 36 such order parameters that provide Lorentz-invariant mass-gaps to Dirac fermions can be organized into a single irreducible tensor representation of the $SO(8)$ symmetry of the two-dimensional Dirac Hamiltonian for the spin-1/2 lattice fermions. The minimal interacting Lagrangian away from the neutrality point has the $SO(8)$ symmetry reduced to $U(1)\times SU(4)$ by finite chemical potential, and it allows only two independent interaction terms. When the Lagrangian is nearly $SO(8)$-symmetric and the ground state insulating at the neutrality point, we argue it turns superconducting at the critical value of the chemical potential through a ``flop" between the tensor components. The theory is exactly solvable when the $SU(4)$ is generalized to $SU(N)$ and $N$ taken large. A lattice Hamiltonian that may exhibit this transition, parallels with the Gross-Neveu model, and applicability to related electronic systems are briefly discussed.

9 pages, including 4.5 pages of supplemental material

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Cited by in corpus (8)

• Gross-Neveu-Yukawa theory of $\text{SO}(2N)\to \text{SO}(N)\times \text{SO}(N)$ spontaneous symmetry breaking
• Spontaneous breaking of the $\text{SO}(2N)$ symmetry in the Gross-Neveu model
• Gross-Neveu-Yukawa SO(2) and SO(3) tensorial criticality
• Emergence of charge density wave and superconducting phase transitions through Lorentz-invariant interactions in the Haldane-Hubbard model
• Beyond one-loop calculation: Higher-order effects on Gross-Neveu-Yukawa tensorial criticality
• Superconductivity in Luttinger semimetals near the SU(4) limit
• Phase transitions on the dark side of the Gross-Neveu model: Spontaneous $\text{O}(4N)$ symmetry breaking at repulsive coupling
• Spontaneous symmetry breaking of $\mathrm{SO}(2N)$ in Gross--Neveu theory from $2+\epsilon$ expansion