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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• 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 (69)

• The Gross-Neveu-Yukawa Archipelago
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• Designer Monte Carlo Simulation for Gross-Neveu Transition
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• Large $N_f$ quantum field theory
• Fermions in Boundary Conformal Field Theory : Crossing Symmetry and $\epsilon$-Expansion
• Line Defect RG Flows in the $\epsilon$ Expansion
• Dirac fermions with plaquette interactions. I. SU(2) phase diagram with Gross-Neveu and deconfined quantum criticalities
• Chiral Ising Gross-Neveu criticality of a single Dirac cone: A quantum Monte Carlo study
• Dirac fermions with plaquette interactions. II. SU(4) phase diagram with Gross-Neveu criticality and quantum spin liquid
• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Momentum dependence of quantum critical Dirac systems
• Nematic Quantum Criticality in Dirac Systems
• Fermion Traces Without Evanescence
• Wilson-Fisher fixed points in presence of Dirac fermions
• Fermion-induced quantum critical point in Dirac semimetals: a sign-problem-free quantum Monte Carlo study
• Emus live on the Gross-Neveu-Yukawa archipelago
• Twisted bilayer graphene at charge neutrality: competing orders of SU(4) Dirac fermions
• Angle-Tuned Gross-Neveu Quantum Criticality in Twisted Bilayer Graphene: A 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
• Phase diagrams of SO($N$) Majorana-Hubbard models: Dimerization, internal symmetry breaking, and fluctuation-induced first-order transitions
• Relativistic Mott transitions and finite-temperature effects of quantum criticality in Dirac semimetals
• Twist-tuned quantum criticality in moiré bilayer graphene
• Quantum Criticality of Anti-ferromagnetism and Superconductivity with Relativity
• Gross-Neveu-Yukawa theory of $\text{SO}(2N)\to \text{SO}(N)\times \text{SO}(N)$ spontaneous symmetry breaking
• Slightly broken higher-spin current in bosonic and fermionic QED in the large-$N$ limit
• Superconducting phase transition in planar fermionic models with Dirac cone tilting
• The fate of non-supersymmetric Gross-Neveu-Yukawa fixed point in two dimensions
• Gross-Neveu-XY quantum criticality in moiré Dirac materials
• Spontaneous breaking of the $\text{SO}(2N)$ symmetry in the Gross-Neveu model
• Absence of SO(4) quantum criticality in Dirac semimetals at two-loop order
• Boosting quantum Monte Carlo and alleviating sign problem by Gutzwiller projection
• Unconventional Gross-Neveu quantum criticality: Interaction-induced SO(3)-biadjoint insulator and emergent SU(3) symmetry
• Experimental validation of nonextensive statistical field theory: applications to manganites
• SO(4) multicriticality of two-dimensional Dirac fermions
• Nonequilibrium Critical Dynamics with Emergent Supersymmetry
• Scale symmetry breaking and generation of mass at quantum critical points
• Is Kaniadakis $\kappa$-generalized statistical mechanics general?
• Chiral critical behavior of 3D lattice fermionic models with quartic interactions
• Five loop renormalization of the Wess-Zumino model
• Fractionalized fermionic multicriticality in anisotropic Kitaev spin-orbital liquids
• Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
• Fermion enhanced first-order phase transition and chiral Gross-Neveu tricritical point
• Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions
• Continued functions and critical exponents: Tools for analytical continuation of divergent expressions in phase transition studies
• Phase diagram and critical behavior of Hubbard model on the square-hexagon-octagon lattice
• Gross-Neveu-Yukawa SO(2) and SO(3) tensorial criticality
• Boundary criticality for the Gross-Neveu-Yukawa models
• Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides
• Anomalous dimensions at small spins
• Emergent Supersymmetry at Large $N$
• Is ${\gamma }_{KLS}$-generalized statistical field theory complete?
• Fermion Bag Approach for Hamiltonian Lattice Field Theories
• Beyond one-loop calculation: Higher-order effects on Gross-Neveu-Yukawa tensorial criticality
• Critical structure and emergent symmetry of Dirac fermion systems
• Fate of surface gaps in magnetic topological insulators
• Fermionic skyrmions and bosonization for a Gross-Neveu transition
• Instabilities of a Generalized Gross-Neveu Quantum Criticality
• Conjecture on the lower bound of the length-scale critical exponent $\nu$ at continuous phase transitions
• On the completeness of the ${\delta }_{KLS}$-generalized statistical field theory
• Renormalization of supersymmetric chiral theories in rational spacetime dimensions
• The Hubbard Model on the Honeycomb Lattice with Hybrid Monte Carlo
• Lattice Field Theory Analysis of the Chiral Heisenberg Model
• Boundary critical behavior of the Gross-Neveu-Yukawa model
• Correction exponents in the chiral Heisenberg model at $1/N^2$: singular contributions and operator mixing
• Spontaneous symmetry breaking of $\mathrm{SO}(2N)$ in Gross--Neveu theory from $2+\epsilon$ expansion
• Fermionic criticality with enlarged fluctuations in Dirac semimetals
• Critical behavior of QED${}_3$--Gross-Neveu-Yukawa Theory in an Arbitrary Gauge