Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone

Abstract

We present quantum Monte Carlo simulations for the chiral Heisenberg Gross-Neveu-Yukawa quantum phase transition of relativistic fermions with $N=4$ Dirac spinor components subject to a repulsive, local four fermion interaction in 2+1$d$. Here we employ a two dimensional lattice Hamiltonian with a single, spin-degenerate Dirac cone, which exactly reproduces a linear energy-momentum relation for all finite size lattice momenta in the absence of interactions. This allows us to significantly reduce finite size corrections compared to the widely studied honeycomb and $\pi$-flux lattices. A Hubbard term dynamically generates a mass beyond a critical coupling of $U_c=6.76(1)$ as the system acquires antiferromagnetic order and SU(2) spin rotational symmetry is spontaneously broken. At the quantum phase transition we extract a self-consistent set of critical exponents $\nu =0.98(1)$, ${\eta }_{\varphi }=0.53(1)$, ${\eta }_{\psi }=0.18(1)$, $\beta =0.75(1)$. We provide evidence for the continuous degradation of the quasi-particle weight of the fermionic excitations as the critical point is approached from the semimetallic phase. Finally we study the effective "speed of light" of the low-energy relativistic description, which depends on the interaction $U$, but is expected to be regular across the quantum phase transition. We illustrate that the strongly coupled bosonic and fermionic excitations share a common velocity at the critical point.

6+6 pages, 12 figures

References in corpus (28)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Tuning superconductivity in twisted bilayer graphene
• Dirac materials
• Interactions and phase transitions on graphene's honeycomb lattice
• Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene
• Theory of interacting electrons on the honeycomb lattice
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Lattice field theory simulations of graphene
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice, with possible applications to twisted bilayer graphene
• Quantum Critical Behaviour in a Graphene-like Model
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Low-dimensional Supersymmetric Lattice Models
• Large $N$ critical exponents for the chiral Heisenberg Gross-Neveu universality class
• Fermion bag approach to Hamiltonian lattice field theories in continuous time
• Anomalous quantum-critical scaling corrections in two-dimensional antiferromagnets
• Gauge-field-assisted Kekulé quantum criticality
• Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice
• Observation of Emergent Spacetime Supersymmetry at Superconducting Quantum Criticality
• Fermion-induced quantum criticality with two length scales in Dirac systems
• Two-Dimensional Wess-Zumino Models at Intermediate Couplings
• From Birefringent Electrons to a Marginal or Non-Fermi Liquid of Relativistic Spin-1/2 Fermions: An Emergent Superuniversality
• Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions
• Critical flavour number of the Thirring model in three dimensions
• Quantum criticality in the metal-superconductor transition of interacting Dirac fermions on a triangular lattice
• Towards Critical Physics in 2+1d with U(2N)-Invariant Fermions
• EMUS-QMC: Elective Momentum Ultra-Size Quantum Monte Carlo Method

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• Duality study of chiral Heisenberg Gross-Neveu model in 1+1 dimensions
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• Twisted bilayer graphene at charge neutrality: competing orders of SU(4) Dirac fermions
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• Relativistic non-Fermi liquid from interacting birefringent fermions: A robust superuniversality
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• Strong-coupling superconductivity near Gross-Neveu quantum criticality in Dirac systems
• Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides
• Response to Comment on "The role of electron-electron interactions in two-dimensional Dirac fermions"
• Critical structure and emergent symmetry of Dirac fermion systems
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• Robust orbital diamagnetism of correlated Dirac fermions in chiral Ising universality class
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