Emus live on the Gross-Neveu-Yukawa archipelago

Abstract

It is expected that the Gross-Neveu-Yukawa (GNY) chiral Ising transition of $N$ Majorana (or $N_f=N/4$ four-component Dirac) fermions coupled with scalar field in (2+1)D will be the first fermionic quantum critical point that various methods such as conformal bootstrap [1], perturbative renormalization group [2] and quantum Monte Carlo (QMC) simulations [3], would yield the converged critical exponents -- serving the same textbook role as the Ising and $O(N)$ models in the statistical and quantum phase transition. However, such expectation has not been fully realized from the lattice QMC simulations due to the obstacles introduced by the UV finite size effect. In this work, by means of the elective-momentum ultra-size (EMUS) QMC method [4], we compute the critical exponents of the GNY $N=8$ chiral Ising transition on a 2D $\pi$-flux fermion lattice model between Dirac semimetal and quantum spin Hall insulator phases [3, 5]. With the matching of fermionic and bosonic momentum transfer and collective update in momentum space, our QMC results provide the fully consistent exponents with those obtained from the bootstrap and perturbative approaches. In this way, the Emus now live happily on the $N=8$ island and could explore the Gross-Neveu-Yukawa archipelago [1] with ease.

6 pages + 3 pages supplementary material, 3 figures

References in corpus (24)

• Moiré heterostructures as a condensed matter quantum simulator
• Topological kagome magnets and superconductors
• Interactions and phase transitions on graphene's honeycomb lattice
• Theory of interacting electrons on the honeycomb lattice
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Ising exponents from the functional renormalisation group
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Four loop renormalization of the Gross-Neveu model
• Massive fermions without fermion bilinear condensates
• The Gross-Neveu-Yukawa Archipelago
• Quantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations
• Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities
• Designer Monte Carlo Simulation for Gross-Neveu Transition
• Dynamical properties of collective excitations in twisted bilayer Graphene
• Superconductivity and bosonic fluid emerging from Moiré flat bands
• 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
• Dirac fermions with plaquette interactions. III. SU(N) phase diagram with Gross-Neveu criticality and first-order phase transition
• Nematic Quantum Criticality in Dirac Systems
• Projection of Infinite-$U$ Hubbard Model and Algebraic Sign Structure
• Validity of SLAC fermions for the (1 + 1)-dimensional helical Luttinger liquid
• A Sport and a Pastime: Model Design and Computation in Quantum Many-Body Systems
• Chiral critical behavior of 3D lattice fermionic models with quartic interactions

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• Evolution of entanglement entropy at SU($N$) deconfined quantum critical points
• An integral algorithm of exponential observables for interacting fermions in quantum Monte Carlo simulation
• Entanglement Microscopy: Tomography and Entanglement Measures via Quantum Monte Carlo
• 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
• Absence of SO(4) quantum criticality in Dirac semimetals at two-loop order
• Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
• Instabilities of a Generalized Gross-Neveu Quantum Criticality
• Addressing the Infinite Variance Problem in Fermionic Monte Carlo Simulations: Retrospective Error Remediation and the Exact Bridge Link Method