Four-loop critical exponents for the Gross-Neveu-Yukawa models

Abstract

We study the chiral Ising, the chiral XY and the chiral Heisenberg models at four-loop order with the perturbative renormalization group in $4-\epsilon$ dimensions and compute critical exponents for the Gross-Neveu-Yukawa fixed points to order $\mathcal{O}({\epsilon }^4)$. Further, we provide Padé estimates for the correlation length exponent, the boson and fermion anomalous dimension as well as the leading correction to scaling exponent in 2+1 dimensions. We also confirm the emergence of supersymmetric field theories at four loops for the chiral Ising and the chiral XY models with $N=1/4$ and $N=1/2$ fermions, respectively. Furthermore, applications of our results relevant to various quantum transitions in the context of Dirac and Weyl semimetals are discussed, including interaction-induced transitions in graphene and surface states of topological insulators.

18 pages, 1 figure, 3 supplemental files attached containing the critical exponents for general number of fermion flavors for each of the models

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• Dirac materials
• Topological Mott Insulators
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• Quantum superconducting criticality in graphene and topological insulators
• Four loop renormalization of the Gross-Neveu model
• Ising and Gross-Neveu model in next-to-leading order
• Multi-meson Yukawa interactions at criticality
• Gauge-field-assisted Kekulé quantum criticality
• The emergence of a universal limiting speed
• Convergence of Derivative Expansion in Supersymmetric Functional RG Flows
• Critical exponent $\omega$ in the Gross-Neveu-Yukawa model at $O(1/N)$

Cited by in corpus (17)

• Designer Monte Carlo Simulation for Gross-Neveu Transition
• Large $N_f$ quantum field theory
• Momentum dependence of quantum critical Dirac systems
• Fermion Traces Without Evanescence
• Fermion-induced quantum critical point in Dirac semimetals: a sign-problem-free quantum Monte Carlo study
• Critical exponent $\eta$ at $O(1/N^3)$ in the chiral XY model using the large $N$ conformal bootstrap
• Fermi-liquid ground state of interacting Dirac fermions in two dimensions
• Gross-Neveu-XY quantum criticality in moiré Dirac materials
• Fermion enhanced first-order phase transition and chiral Gross-Neveu tricritical point
• Continued functions and critical exponents: Tools for analytical continuation of divergent expressions in phase transition studies
• Is ${\gamma }_{KLS}$-generalized statistical field theory complete?
• Fermion Bag Approach for Hamiltonian Lattice Field Theories
• On the completeness of the ${\delta }_{KLS}$-generalized statistical field theory
• Renormalization of supersymmetric chiral theories in rational spacetime dimensions
• Fermionic criticality with enlarged fluctuations in Dirac semimetals
• The Hubbard Model on the Honeycomb Lattice with Hybrid Monte Carlo
• Critical behavior of QED${}_3$--Gross-Neveu-Yukawa Theory in an Arbitrary Gauge