SO(4) multicriticality of two-dimensional Dirac fermions

Abstract

We study quantum multicritical behavior in a (2+1)-dimensional Gross-Neveu-Yukawa field theory with eight-component Dirac fermions coupled to two triplets of order parameters that act as Dirac masses, and transform as $(1,0)+(0,1)$ representation under the SO(4)$\simeq$SO(3)$\times$SO(3) symmetry group. This field theory is relevant to spin-1/2 fermions on honeycomb or $\pi$-flux lattices, for example, near the transition points between an $s$-wave superconductor and a charge-density wave, on one side, and Néel order, on the other. Two triplets of such order parameters always allow for a common pair of two other order parameters that would complete them to the maximal set of compatible (anticommuting) orders of five. We first derive a unitary transformation in the Nambu (particle-hole) space which maps any two such triplets, possibly containing some superconducting orders, onto purely insulating order parameters. This allows one to consider a universal SO(4) Gross-Neveu-Yukawa description of the multicriticality without any Nambu doubling. We then proceed to derive the renormalization-group flow of the coupling constants at one-loop order in $4-\epsilon$ space-time dimensions, allowing also a more general set of order parameters transforming under SO($n_a$)$\times$SO($n_b$). While for $n_a=n_b>2$ in the bosonic sector and with fermions decoupled there is a stable fixed point of the flow, the Yukawa coupling to fermions quickly leads to its elimination by a generic fixed-point collision in the relevant range of fermion flavor numbers $N_f$. This suggests the replacement of the critical behavior by a runaway flow in the physical case $n_a=n_b=3$. The structure of the RG flow at $n_a\ne n_b$ is also discussed, and some non-perturbative arguments in favor of the stability of the decoupled critical point when $n_a=3$ and $n_b=1$ in $D=2+1$ are provided.

13 pages, 4 figures

References in corpus (16)

• Interactions and phase transitions on graphene's honeycomb lattice
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Theory of interacting electrons on the honeycomb lattice
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Topological Mott insulator in three-dimensional systems with quadratic band touching
• Quantum superconducting criticality in graphene and topological insulators
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Chiral symmetry breaking in ${\mathrm{QED}}_3$ in presence of irrelevant interactions: a renormalization group study
• Critical behavior of the (2+1)-dimensional Thirring model
• Phase diagram of electronic systems with quadratic Fermi nodes in $2<d<4$: $2+\epsilon$ expansion, $4-\epsilon$ expansion, and functional renormalization group
• Ising and Gross-Neveu model in next-to-leading order
• Gauge-field-assisted Kekulé quantum criticality
• Effect of short-range interactions on the quantum critical behavior of spinless fermions on the honeycomb lattice
• Fermion-induced quantum critical point in Dirac semimetals: a sign-problem-free quantum Monte Carlo study
• Fermion enhanced first-order phase transition and chiral Gross-Neveu tricritical point