Dirac electrons in the square lattice Hubbard model with a $d$-wave pairing field: chiral Heisenberg universality class revisited

Abstract

We numerically investigate the quantum criticality of the chiral Heisenberg universality class with the total number of fermion components $N$=8 in terms of the Gross-Neveu theory. Auxiliary-field quantum Monte Carlo simulations are performed for the square lattice Hubbard model in the presence of a $d$-wave pairing field, inducing Dirac cones in the single particle spectrum. This property makes the model particularly interesting because it turns out to belong to the same universality class of the Hubbard model on the honeycomb lattice, that is the canonical model for graphene, despite the unit cells being apparently different (e.g. they contain one and two sites, respectively). We indeed show that the two phase transitions, expected to occur on the square and on the honeycomb lattices, have the same quantum criticality. We also argue that details of the models, i.e., the way of counting $N$ and the anisotropy of the Dirac cones, do not change the critical exponents. The present estimates of the exponents for the $N$=8 chiral Heisenberg universality class are $\nu$=1.05(5), ${\eta }_{\varphi }$=0.75(4), and ${\eta }_{\psi }$=0.23(4), which are compared with the previous numerical estimations.

arXiv comment12 pages, 12 figures

References in corpus (60)

• Dirac materials
• Dirac Fermions in Solids - from High Tc cuprates and Graphene to Topological Insulators and Weyl Semimetals
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Interactions and phase transitions on graphene's honeycomb lattice
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Is graphene in vacuum an insulator?
• Theory of interacting electrons on the honeycomb lattice
• Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
• Quantum criticality with two length scales
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Relativistic Mott criticality in graphene
• Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons
• Masses in graphene-like two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics
• Ground state and finite temperature signatures of quantum phase transitions in the half-filled Hubbard model on a honeycomb lattice
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• High-precision finite-size scaling analysis of the quantum-critical point of S=1/2 Heisenberg antiferromagnetic bilayers
• Quantum phase transitions in d-wave superconductors
• Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice, with possible applications to twisted bilayer graphene
• Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach
• Computation of Critical Exponent ηat O(1/N^3) in the Four Fermi Model in Arbitrary Dimensions
• Fermion-induced quantum critical points
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Phase transition and critical behaviour of the d=3 Gross-Neveu model
• Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions
• Critical Behaviour of the 3d Gross-Neveu and Higgs-Yukawa Models
• Bayesian Inference in the Scaling Analysis of Critical Phenomena
• Critical exponents of the Gross-Neveu model from the effective average action
• Superconductivity from the Condensation of Topological Defects in a Quantum Spin-Hall Insulator
• Counting Rules of Nambu-Goldstone Modes
• Thermal Ising transitions in the vicinity of two-dimensional quantum critical points
• Critical behavior of Dirac fermions from perturbative renormalization
• Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
• Comprehensive quantum Monte Carlo study of the quantum critical points in planar dimerized/quadrumerized Heisenberg models
• Interaction induced Dirac fermions from quadratic band touching in bilayer graphene
• The intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model
• Emergent Lorentz symmetry near fermionic quantum critical points in two and three dimensions
• Fermion-induced quantum criticality in two-dimensional Dirac semimetals: Non-perturbative flow equations, fixed points and critical exponents
• Large $N$ critical exponents for the chiral Heisenberg Gross-Neveu universality class
• Spin nematics, valence-bond solids and spin liquids in SO($N$) quantum spin models on the triangular lattice
• Anomalous quantum-critical scaling corrections in two-dimensional antiferromagnets
• Relativity Restored: Dirac Anisotropy in QED${}_3$
• Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• The Semimetal-Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice
• Incipient nodal pairing in planar d-wave superconductors
• Designer Monte Carlo Simulation for Gross-Neveu Transition
• Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions
• Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality
• Quantum criticality in the metal-superconductor transition of interacting Dirac fermions on a triangular lattice
• Influence of Coulomb interaction on the anisotropic Dirac cone in graphene
• Stochastic series expansion simulation of the $t$-$V$ model
• Mott physics in the half-filled Hubbard model on a family of vortex-full square lattices
• Mott Transition in the Two-Dimensional Flux Phase
• Subtlety of Determining the Critical Exponent $\nu$ of the Spin-1/2 Heisenberg Model with a Spatially Staggered Anisotropy on the Honeycomb Lattice
• Criticality and scaling corrections for two-dimensional Heisenberg models in plaquette patterns with strong and weak couplings
• Fermion-induced quantum critical point in Dirac semimetals: a sign-problem-free quantum Monte Carlo study
• Fermi-liquid ground state of interacting Dirac fermions in two dimensions
• Topological terms on topological defects: a quantum Monte Carlo study
• Anisotropy on the Fermi Surface of the Two-Dimensional Hubbard Model
• Interacting Anisotropic Dirac Fermions in Strained Graphene and Related Systems

Cited by in corpus (30)

• The Semimetal-Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice
• Competing nodal d-wave superconductivity and antiferromagnetism
• Magnetism and charge order in the honeycomb lattice
• Universality and Critical Exponents of the Fermion Sign Problem
• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Gross-Neveu Heisenberg criticality: dynamical generation of quantum spin Hall masses
• Gross-Neveu-Heisenberg criticality from competing nematic and antiferromagnetic orders in bilayer graphene
• Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation
• Wilson-Fisher fixed points in presence of Dirac fermions
• Semigroup approach to the sign problem in quantum Monte Carlo simulations
• Angle-Tuned Gross-Neveu Quantum Criticality in Twisted Bilayer Graphene: A Quantum Monte Carlo Study
• Twisted bilayer graphene at charge neutrality: competing orders of SU(4) Dirac fermions
• Relativistic Mott transitions and finite-temperature effects of quantum criticality in Dirac semimetals
• Quantum Criticality of Anti-ferromagnetism and Superconductivity with Relativity
• Absence of SO(4) quantum criticality in Dirac semimetals at two-loop order
• SO(4) multicriticality of two-dimensional Dirac fermions
• Chiral critical behavior of 3D lattice fermionic models with quartic interactions
• The extended Hubbard model on a honeycomb lattice
• Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
• QMC study of the chiral Heisenberg Gross-Neveu universality class
• Emergent Anti-ferromagnetism in a Y -Shaped Kekulé Graphene
• Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions
• Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides
• Fermionic skyrmions and bosonization for a Gross-Neveu transition
• Quantum conditional mutual information as a probe of measurement-induced entanglement phase transitions
• The Hubbard Model on the Honeycomb Lattice with Hybrid Monte Carlo
• Hubbard Model on the Honeycomb Lattice with an Indefinite Long-Range Interaction
• Emergence of topological defects and spin liquid in a two-orbital spin-fermion model on the honeycomb lattice
• Lattice Field Theory Analysis of the Chiral Heisenberg Model
• Spin-orbit coupled periodic Anderson model: Kondo-Dirac semimetal and orbital-selective antiferromagnetic semimetal