Caution on Gross-Neveu criticality with a single Dirac cone: Violation of locality and its consequence of unexpected finite-temperature transition

Abstract

Lately there are many SLAC fermion investigations on the (2+1)D Gross-Neveu criticality of a single Dirac cone [1,2]. While the SLAC fermion construction indeed gives rise to the linear energy-momentum relation for all lattice momenta at the non-interacting limit, the long-range hopping and its consequent violation of locality on the Gross-Neveu quantum critical point (GN-QCP) -- which a priori requires short-range interaction -- has not been verified. Here we show, by means of large-scale quantum Monte Carlo simulations, that the interaction-driven antiferromagnetic insulator in this case is fundamentally different from that on a purely local $\pi$-flux Hubbard model on the square lattice. In particular, we find the antiferromagnetic long-range order in the SLAC fermion model has a finite temperature continuous phase transition, which violates the Mermin-Wagner theorem, and smoothly connects to the previously determined GN-QCP. The magnetic excitations inside the antiferromagnetic insulator are gapped without Goldstone mode, even though the state spontaneously breaks continuous $SU(2)$ symmetry. These unusual results proclaim caution on the interpretation of the quantum phase transition in SLAC fermion model as that of GN-QCP with short-range interaction.

References in corpus (48)

• The electronic properties of graphene
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Theory of Underdoped Cuprates
• U(1) Gauge Theory of the Hubbard Model : Spin Liquid States and Possible Application to k-(BEDT-TTF)_2 Cu_2 (CN)_3
• Algebraic spin liquid as the mother of many competing orders
• A sufficient condition for the absence of the sign problem in the fermionic quantum Monte-Carlo algorithm
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons
• Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice, with possible applications to twisted bilayer graphene
• Phase diagram of the half-filled two-dimensional SU(N) Hubbard-Heisenberg model: a quantum Monte Carlo study
• Duality between the deconfined quantum-critical point and the bosonic topological transition
• Dynamical Signature of Fractionalization at the Deconfined Quantum Critical Point
• Correlation-induced insulating topological phases at charge neutrality in twisted bilayer graphene
• Is magic-angle twisted bilayer graphene near a quantum critical point?
• Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: the Parent State of Quantum Phases
• Superconductivity from the Condensation of Topological Defects in a Quantum Spin-Hall Insulator
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Permanent confinement in the compact QED3 with fermionic matter
• On the Hohenberg-Mermin-Wagner theorem and its limitations
• Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
• Phases of the (2+1) dimensional SO(5) non-linear sigma model with topological term
• Interaction induced Dirac fermions from quadratic band touching in bilayer graphene
• Massless Dirac Fermions, Gauge Fields, and Underdoped Cuprates
• Quantum disordered phase near the Mott transition in the staggered-flux Hubbard model on a square lattice
• Quantum spin chains with site dissipation
• Designer Monte Carlo Simulation for Gross-Neveu Transition
• Bootstrapping $N_f=4$ conformal QED${}_3$
• Numerical determination of monopole scaling dimension in parity-invariant three-dimensional non-compact QED
• Correlated Insulating Phases in the Twisted Bilayer Graphene
• Doping-induced quantum spin Hall insulator to superconductor transition
• Quantum phase transitions in Dirac fermion systems
• Dissipation-Induced Order: The $S=1/2$ Quantum Spin Chain Coupled to an Ohmic Bath
• Local Quantum Criticality in the Two-dimensional Dissipative Quantum XY Model
• Erratum: algebraic spin liquid as the mother of many competing orders
• Generalized Higgs mechanism in long-range interacting quantum systems
• Metallic and Deconfined Quantum Criticality in Dirac Systems
• 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
• Quantum criticality in the two-dimensional dissipative quantum XY model-II
• Compact quantum electrodynamics in 2+1 dimensions and spinon deconfinement: a renormalization group analysis
• Dirac fermions with plaquette interactions. II. SU(4) phase diagram with Gross-Neveu criticality and quantum spin liquid
• Anomalous dimensions of monopole operators at the transitions between Dirac and topological spin liquids
• Dynamical properties of quantum many-body systems with long range interactions
• Dirac fermions with plaquette interactions. III. SU(N) phase diagram with Gross-Neveu criticality and first-order phase transition
• QED${}_3$-inspired three-dimensional conformal lattice gauge theory without fine-tuning
• Validity of SLAC fermions for the (1 + 1)-dimensional helical Luttinger liquid

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• Unconventional Scalings of Quantum Entropies in Long-Range Heisenberg Chains
• Nonequilibrium Critical Dynamics with Emergent Supersymmetry
• Helical Luttinger liquid on a space-time lattice
• Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions
• Nature of the Topological Transition of the Kitaev Model in [111] Magnetic Field
• Fermionic skyrmions and bosonization for a Gross-Neveu transition