Lattice field theory simulations of graphene

Abstract

We discuss the Monte Carlo method of simulating lattice field theories as a means of studying the low-energy effective theory of graphene. We also report on simulational results obtained using the Metropolis and Hybrid Monte Carlo methods for the chiral condensate, which is the order parameter for the semimetal-insulator transition in graphene, induced by the Coulomb interaction between the massless electronic quasiparticles. The critical coupling and the associated exponents of this transition are determined by means of the logarithmic derivative of the chiral condensate and an equation-of-state analysis. A thorough discussion of finite-size effects is given, along with several tests of our calculational framework. These results strengthen the case for an insulating phase in suspended graphene, and indicate that the semimetal-insulator transition is likely to be of second order, though exhibiting neither classical critical exponents, nor the predicted phenomenon of Miransky scaling.

14 pages, 7 figures. Published version freely available if accessed via http://physics.aps.org/articles/v2/30

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Cited by in corpus (137)

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• Electronic Properties of Graphene in a Strong Magnetic Field
• Dirac materials
• Dirac Fermions in Solids - from High Tc cuprates and Graphene to Topological Insulators and Weyl Semimetals
• Artificial graphene as a tunable Dirac material
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Chiral d-wave superconductivity in doped graphene
• Ferromagnetic and antiferromagnetic order in bacterial vortex lattices
• Relativistic Mott criticality in graphene
• RKKY coupling in graphene
• Monte-Carlo study of the semimetal-insulator phase transition in monolayer graphene with realistic inter-electron interaction potential
• Gap generation and semimetal-insulator phase transition in graphene
• Supercritical Coulomb center and excitonic instability in graphene
• Monte Carlo Simulation of the Semimetal-Insulator Phase Transition in Monolayer Graphene
• Intrinsic plasmons in 2D Dirac materials
• Coulomb interaction in graphene: Relaxation rates and transport
• On the Phase Structure of Many-Flavor QED${}_3$
• Coulomb interaction at the metal-insulator critical point in graphene
• Monte-Carlo study of the electron transport properties of monolayer graphene within the tight-binding model
• Quantum critical behavior in three dimensional lattice Gross-Neveu models
• Critical exponents of the semimetal-insulator transition in graphene: A Monte Carlo study
• Two-body problem in graphene
• Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
• Monte-Carlo simulation of the tight-binding model of graphene with partially screened Coulomb interactions
• Effective field theory, three-loop perturbative expansion, and their experimental implications in graphene many-body effects
• The intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model
• Pseudospin Order in Monolayer, Bilayer, and Double-Layer Graphene
• Lattice methods for strongly interacting many-body systems
• Quantum phases of interacting electrons in three-dimensional dirty Dirac semimetals
• Geometrical and topological aspects of graphene and related materials
• Optical Response and Ground State of Graphene
• Interaction and excitonic insulating transition in graphene
• Fermion bag approach to Hamiltonian lattice field theories in continuous time
• Chiral Symmetry Breaking and the Quantum Hall Effect in Monolayer Graphene
• The importance of electron-electron interactions in the RKKY coupling in graphene
• Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice
• Excitonic condensation in a double-layer graphene system
• Fermi velocity renormalization and dynamical gap generation in graphene
• Dynamics of electric transport in interacting Weyl semimetals
• Absence of dynamical gap generation in suspended graphene
• Chiral Gap and Collective Excitations in Monolayer Graphene from Strong Coupling Expansion of Lattice Gauge Theory
• Interplay between sublattice and spin symmetry breaking in graphene
• Many-body effects in graphene beyond the Dirac model with Coulomb interaction
• Monte Carlo simulation of monolayer graphene at non-zero temperature
• Numerical study of the conductivity of graphene monolayer within the effective field theory approach
• Magnetic field driven instability of charged center in graphene
• Critical behaviour of reduced QED${}_{4,3}$ and dynamical fermion gap generation in graphene
• Chiral anomaly and strength of the electron-electron interaction in graphene
• Correlated Dirac Fermions on the Honeycomb Lattice studied within Cluster Dynamical Mean Field Theory
• The fate of the resonating valence bond in graphene
• Quantum Monte Carlo Calculations for Carbon Nanotubes
• Lattice quantum electrodynamics for graphene
• Renormalization group approach to chiral symmetry breaking in graphene
• Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals
• Tunable edge magnetism at graphene/graphane interfaces
• Weyl Semimetal in the Strong Coulomb Interaction Limit
• A hybrid Monte Carlo approach to the entanglement entropy of interacting fermions
• Enhancement of non-local exchange near isolated band-crossings in graphene
• Numerical evidence of conformal phase transition in graphene with long-range interactions
• Artifical atoms in interacting graphene quantum dots
• Effect of Coulomb interactions on the physical observables of graphene
• Zero-modes and global antiferromagnetism in strained graphene
• Influence of Coulomb interaction on the anisotropic Dirac cone in graphene
• Excitonic Effects in Two-Dimensional Massless Dirac Fermions
• Quantum Monte Carlo study of static potential in graphene
• Few-fermion systems in one dimension: Ground- and excited-state energies and contacts
• Chiral-Symmetry Breaking in Pseudo Quantum Electrodynamics at Finite Temperature
• 1/N Expansion in Correlated Graphene
• Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultra-relativistic limit of Dirac liquids
• Chiral Symmetry Breaking in Monolayer Graphene by Strong Coupling Expansion of Compact and Non-compact U(1) Lattice Gauge Theories
• Stability of Multinode Dirac Semimetals against Strong Long-Range Correlations
• Renormalization of the band gap in 2D materials through the competition between electromagnetic and four-fermion interactions
• Finite-size version of the excitonic instability in graphene quantum dots
• Tilted Dirac cone effects and chiral symmetry breaking in a planar four-fermion model
• Catalysis of Dynamical Chiral Symmetry Breaking by Chiral Chemical Potential in Dirac semimetals
• Valley-dependent spin-orbit torques in two dimensional hexagonal crystals
• Magnetic Catalysis in Graphene Effective Field Theory
• Non-perturbative renormalization group calculation of the quasi-particle velocity and the dielectric function of graphene
• Monte-Carlo study of Dirac semimetals phase diagram
• Dynamical fermion mass generation and exciton spectra in graphene
• Excitonic mass gap in uniaxially strained graphene
• Eliashberg theory of excitonic insulating transition in graphene
• Numerical simulation of graphene in external magnetic field
• Lattice Field Theory Study of Magnetic Catalysis in Graphene
• Chiral symmetry restoration in monolayer graphene induced by Kekule distortion
• Phase structure of 2-dimensional topological insulators by lattice strong coupling expansion
• Zero-energy vortices in Dirac materials
• Phase structure of monolayer graphene from effective U(1) gauge theory on honeycomb lattice
• Effects of flavor-symmetry violation from staggered fermion lattice simulations of graphene
• The effect of vertex corrections on the possibility of chiral symmetry breaking, induced by long-range Coulomb repulsion in graphene
• Strong Coupling Expansion in a Correlated Three-Dimensional Topological Insulator
• Accelerating Hybrid Monte Carlo simulations of the Hubbard model on the hexagonal lattice
• Chiral condensate with topological degeneracy in graphene and its manifestation in edge states
• Semi-metal-insulator transition on the surface of a topological insulator with in-plane magnetization
• The possibility of measuring intrinsic electronic correlations in graphene using a d-wave contact Josephson junction
• Impurity effects and bandgap-closing in massive Dirac systems
• Screening and gap generation in bilayer graphene
• Dynamical gap generation in 2D Dirac semimetal with deformed Dirac cone
• Competition between excitonic gap generation and disorder scattering in graphene
• Applications of lattice QCD techniques for condensed matter systems
• Equations of motion method for triplet excitation operators in graphene
• Emergent Spin Liquids in the Hubbard Model on the Anisotropic Honeycomb Lattice
• Chiral Symmetry Breaking in Planar QED in External Magnetic Fields
• Coulomb interaction and semimetal-insulator transition in graphene
• A Hybrid-Monte-Carlo study of monolayer graphene with partially screened Coulomb interactions at finite spin density
• Inelastic electron tunneling spectroscopy at local defects in graphene
• Field theoretic study of electron-electron interaction effects in Dirac liquids
• Dyson-Schwinger approach to strongly coupled theories
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• Interaction of static charges in graphene within Monte-Carlo simulation
• Lattice field theory simulations of Dirac semimetals
• Phase Diagram Structure of Topological Mott Transition for Zero-gap Semiconductors beyond Conventional Landau-Ginzburg-Wilson Scenario
• Toward large-scale Hybrid Monte Carlo simulations of the Hubbard model on graphics processing units
• Mean-field quantum phase transition in graphene and in general gapless systems
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• Magnetic, charge, and transport properties of graphene nanoflakes
• Robustness of the semimetal state of Na3Bi and Cd3As2 against Coulomb interaction
• Fermi point in graphene as a monopole in momentum space
• Monte Carlo Study of Strongly-Interacting Degenerate Fermions: a Model for Voltage-Biased Bilayer Graphene
• First order phase transitions within Weyl type of materials at low temperatures
• Hybrid Monte-Carlo simulation of interacting tight-binding model of graphene
• Quantum critical phenomena of the excitonic insulating transition in two dimensions
• Reduced QED with few planes and fermion gap generation
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• Beth-Uhlenbeck equation for the thermodynamics of fluctuations in a generalised 2+1D Gross-Neveu model
• Electronic structure of semiconductor nanoparticles from stochastic evaluation of imaginary-time path integral
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• Strong Interaction Effects at a Fermi Surface in a Model for Voltage-Biased Bilayer Graphene
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• Monte-Carlo study of quasiparticle dispersion relation in monolayer graphene
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• Chiral Symmetry and Many-Body Effect in Multilayer Graphene