The Antiferromagnetic Character of the Quantum Phase Transition in the Hubbard Model on the Honeycomb Lattice

Abstract

We provide a unified, comprehensive treatment of all operators that contribute to the anti-ferromagnetic, ferromagnetic, and charge-density-wave structure factors and order parameters of the hexagonal Hubbard Model. We use the Hybrid Monte Carlo algorithm to perform a systematic, carefully controlled analysis in the temporal Trotter error and of the thermodynamic limit. We expect our findings to improve the consistency of Monte Carlo determinations of critical exponents. We perform a data collapse analysis and determine the critical exponent $\beta =0.898(37)$ for the semimetal-Mott insulator transition in the hexagonal Hubbard Model. Our methods are applicable to a wide range of lattice theories of strongly correlated electrons.

References in corpus (25)

• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Solving Lattice QCD systems of equations using mixed precision solvers on GPUs
• Interactions and phase transitions on graphene's honeycomb lattice
• High density QCD on a Lefschetz thimble?
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Speeding up the Hybrid-Monte-Carlo algorithm for dynamical fermions
• Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
• Quantum criticality with two length scales
• Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons
• Stochastic Estimation with $Z_2$ Noise
• Ground state and finite temperature signatures of quantum phase transitions in the half-filled Hubbard model on a honeycomb lattice
• Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach
• Structure of Lefschetz thimbles in simple fermionic systems
• Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons
• Revisiting the Hybrid Quantum Monte Carlo Method for Hubbard and Electron-Phonon Models
• Charge Order in the Holstein Model on a Honeycomb Lattice
• Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice
• Lefschetz thimbles decomposition for the Hubbard model on the hexagonal lattice
• The Semimetal-Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice
• Quantum Monte Carlo Calculations for Carbon Nanotubes
• Leveraging Machine Learning to Alleviate Hubbard Model Sign Problems
• Avoiding Ergodicity Problems in Lattice Discretizations of the Hubbard Model
• Accelerating Hybrid Monte Carlo simulations of the Hubbard model on the hexagonal lattice
• Electronic Ground State in Bilayer Graphene with Realistic Coulomb Interactions
• Extracting the Single-Particle Gap in Carbon Nanotubes with Lattice Quantum Monte Carlo

Cited by in corpus (8)

• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Non-Hertz-Millis scaling of the antiferromagnetic quantum critical metal via scalable Hybrid Monte Carlo
• Phase diagram of the Hubbard model on a honeycomb lattice: A cluster slave-spin study
• SO(4) multicriticality of two-dimensional Dirac fermions
• Localization of Electronic States in Hybrid Nano-Ribbons in the Non-Perturbative Regime
• QMC study of the chiral Heisenberg Gross-Neveu universality class
• Emergent Anti-ferromagnetism in a Y -Shaped Kekulé Graphene
• The Semimetal-Antiferromagnetic Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice