Beyond one-loop calculation: Higher-order effects on Gross-Neveu-Yukawa tensorial criticality

Abstract

We study the Gross-Neveu-Yukawa field theory for the SO($N$) symmetric traceless rank-two tensor order parameter coupled to Majorana fermions using the $\epsilon$-expansion around upper critical dimensions of $3+1$ to two loops. Previously we established in the one-loop calculation that the theory does not exhibit a critical fixed point for $N\ge 4$, but that nevertheless the stable fixed point inevitably emerges at a large number of fermion flavors $N_f$. For $N_f<N_{f,c1}\approx N/2$, no critical fixed point exists; for $N_{f,c1}<N_f<N_{f,c2}$, a real critical fixed point emerges from the complex plane but fails to satisfy the additional stability conditions necessary for a continuous phase transition; and finally only for $N_f>N_{f,c2}\approx N$, the fixed point satisfies the stability conditions as well. In the present work we compute the $O(\epsilon )$ (two-loop) corrections to the critical flavour numbers $N_{f,c1}$ and $N_{f,c2}$. Most importantly, we observe a sharp decrease in $N_{f,c2}$ from its one-loop value, which brings it closer to the point $N_f=1$ relevant to the standard Gross-Neveu model. Some three-loop results are also presented and discussed.

12 page, 3 figures

References in corpus (26)

• Interactions and phase transitions on graphene's honeycomb lattice
• Theory of interacting electrons on the honeycomb lattice
• Relativistic Mott criticality in graphene
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Renormalization group theory of nematic ordering in d-wave superconductors
• Quantum superconducting criticality in graphene and topological insulators
• Gross-Neveu-Yukawa model at three loops and Ising critical behavior of Dirac systems
• Abelian Higgs model at four loops, fixed-point collision and deconfined criticality
• Critical behavior of Dirac fermions from perturbative renormalization
• Renormalization group analysis of quantum critical points in d-wave superconductors
• The Gross-Neveu-Yukawa Archipelago
• Gauge-field-assisted Kekulé quantum criticality
• Fermion-induced quantum criticality with two length scales in Dirac systems
• Criticality of O(N) symmetric models in the presence of discrete gauge symmetries
• Bootstrapping traceless symmetric $O(N)$ scalars
• Tensor $O(N)$ model near six dimensions: fixed points and conformal windows from four loops
• Nematic Quantum Criticality in Dirac Systems
• Wilson-Fisher fixed points in presence of Dirac fermions
• Long-range Coulomb Interaction effects on Topological Phase Transitions between Semi-metals and Insulators
• $SO(8)$ unification and the large-N theory of superconductor-insulator transition of two-dimensional Dirac fermions
• Phase diagrams of SO($N$) Majorana-Hubbard models: Dimerization, internal symmetry breaking, and fluctuation-induced first-order transitions
• Critical properties of metallic and deconfined quantum phase transitions in Dirac systems
• Gross-Neveu-Yukawa theory of $\text{SO}(2N)\to \text{SO}(N)\times \text{SO}(N)$ spontaneous symmetry breaking
• Note on "Quantum superconducting criticality in graphene and topological insulators"
• Spontaneous breaking of the $\text{SO}(2N)$ symmetry in the Gross-Neveu model
• Gross-Neveu-Yukawa SO(2) and SO(3) tensorial criticality

Cited by in corpus (1)

• Phase transitions on the dark side of the Gross-Neveu model: Spontaneous $\text{O}(4N)$ symmetry breaking at repulsive coupling