Designer Monte Carlo Simulation for Gross-Neveu Transition
arXiv:1910.07430 · doi:10.1103/PhysRevB.101.064308
Abstract
In this manuscript, we study quantum criticality of Dirac fermions via large-scale numerical simulations, focusing on the Gross-Neveu-Yukawa(GNY) chiral-Ising quantum critical point with critical bosonic modes coupled with Dirac fermions. We show that finite-size effects at this quantum critical point can be efficiently minimized via model design, which maximizes the ultraviolet cutoff and at the same time places the bare control parameters closer to the nontrivial fixed point to better expose the critical region. Combined with the efficient self-learning quantum Monte Carlo algorithm, which enables non-local update of the bosonic field, we find that moderately-large system size (up to ) is already sufficient to produce robust scaling behavior and critical exponents.The conductance of the Dirac fermions is also calculated and its frequency dependence is found to be consistent with the scaling behavior predicted by the conformal field theory. The methods and model-design principles developed for this study can be generalized to other fermionic QCPs, and thus provide a promising direction for controlled studies of strongly-correlated itinerant systems.
arXiv comment11 pages, 6 figures
References in corpus (31)
- Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
- Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order
- Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order
- Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
- Quantum criticality with two length scales
- Self-Learning Monte Carlo Method
- Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons
- Quantum-critical behavior of itinerant ferromagnets
- Four-loop critical exponents for the Gross-Neveu-Yukawa models
- Duality between the deconfined quantum-critical point and the bosonic topological transition
- Ising nematic quantum critical point in a metal: a Monte Carlo study
- The dynamics of quantum criticality via Quantum Monte Carlo and holography
- Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography
- Bootstrapping 3D Fermions with Global Symmetries
- Is magic-angle twisted bilayer graphene near a quantum critical point?
- Quantum critical behavior in three dimensional lattice Gross-Neveu models
- Critical behavior of Dirac fermions from perturbative renormalization
- Self-Learning Determinantal Quantum Monte Carlo Method
- Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
- Universal Conductivity in a Two-Dimensional Superfluid-to-Insulator Quantum Critical System
- Non-Fermi-liquid at (2+1)d ferromagnetic quantum critical point
- Interaction induced Dirac fermions from quadratic band touching in bilayer graphene
- Exact critical exponents for the antiferromagnetic quantum critical metal in two dimensions
- Emergent Lorentz symmetry near fermionic quantum critical points in two and three dimensions
- Quantum critical properties of a metallic spin density wave transition
- Spin conservation and Fermi liquid near a ferromagnetic quantum critical point
- Itinerant quantum critical point with frustration and non-Fermi-liquid
- Revealing Fermionic Quantum Criticality from New Monte Carlo Techniques
- Dynamical Generation of Topological Masses in Dirac Fermions
- Dynamical response near quantum critical points
- EMUS-QMC: Elective Momentum Ultra-Size Quantum Monte Carlo Method
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- Fractionalized fermionic quantum criticality in spin-orbital Mott insulators
- Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities
- New Developments in the Numerical Conformal Bootstrap
- Dirac electrons in the square lattice Hubbard model with a -wave pairing field: chiral Heisenberg universality class revisited
- Correlated Insulating Phases in the Twisted Bilayer Graphene
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- Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality
- Quantum phase transitions in Dirac fermion systems
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- Mixed Scalar-Current bootstrap in three dimensions
- Metallic and Deconfined Quantum Criticality in Dirac Systems
- Confinement transition in the QED-Gross-Neveu-XY universality class
- 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
- Fractionalized quantum criticality in spin-orbital liquids from field theory beyond the leading order
- Gross-Neveu Heisenberg criticality: dynamical generation of quantum spin Hall masses
- Dirac fermions with plaquette interactions. III. SU(N) phase diagram with Gross-Neveu criticality and first-order phase transition
- Metal to Orthogonal Metal Transition
- Nematic Quantum Criticality in Dirac Systems
- Torus Spectroscopy of the Gross-Neveu-Yukawa Quantum Field Theory: Free Dirac versus Chiral Ising Fixed Point
- Entanglement Microscopy: Tomography and Entanglement Measures via Quantum Monte Carlo
- Wilson-Fisher fixed points in presence of Dirac fermions
- Emus live on the Gross-Neveu-Yukawa archipelago
- Angle-Tuned Gross-Neveu Quantum Criticality in Twisted Bilayer Graphene: A Quantum Monte Carlo Study
- Relativistic Mott transitions and finite-temperature effects of quantum criticality in Dirac semimetals
- Fermion-induced quantum critical point in the Landau-Devonshire model
- Caution on Gross-Neveu criticality with a single Dirac cone: Violation of locality and its consequence of unexpected finite-temperature transition
- Network-Initialized Monte Carlo Based on Generative Neural Networks
- Absence of SO(4) quantum criticality in Dirac semimetals at two-loop order
- Chiral critical behavior of 3D lattice fermionic models with quartic interactions
- 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
- Critical structure and emergent symmetry of Dirac fermion systems
- Fermionic criticality with enlarged fluctuations in Dirac semimetals