Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice

Abstract

Using first-principle Hybrid-Monte-Carlo (HMC) simulations, we carry out an unbiased study of the competition between spin-density wave (SDW) and charge-density wave (CDW) order in the extended Hubbard model on the two dimensional hexagonal lattice at half filling. We determine the phase diagram in the space of on-site and nearest-neighbor couplings $U$ and $V$ in the region $V<U/3$, which can be simulated without a fermion sign problem, and find that a transition from semimetal to a SDW phase occurs at sufficiently large $U$ for basically all $V$. Tracing the corresponding phase boundary from $V=0$ to the $V=U/3$ line, we find evidence for critical scaling in the Gross-Neveu universality class for the entire boundary. With rather high confidence we rule out the existence of the CDW ordered phase anywhere in the range of parameters considered. We also discuss several improvements of the HMC algorithm which are crucial to reach these conclusions, in particular the improved fermion action with exact sublattice symmetry and the complexification of the Hubbard-Stratonovich field to ensure the ergodicity of the algorithm.

revised version accepted for publication (three additional figures, one additional table)

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• The Semimetal-Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice
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• Numerical evidence of conformal phase transition in graphene with long-range interactions
• The Antiferromagnetic Character of the Quantum Phase Transition in the Hubbard Model on the Honeycomb Lattice
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• Avoiding Ergodicity Problems in Lattice Discretizations of the Hubbard Model
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• Gross-Neveu-Heisenberg criticality from competing nematic and antiferromagnetic orders in bilayer graphene
• Critical properties of the Néel/algebraic-spin-liquid transition
• Non-Hertz-Millis scaling of the antiferromagnetic quantum critical metal via scalable Hybrid Monte Carlo
• A density of states approach to the hexagonal Hubbard model at finite density
• Angle-Tuned Gross-Neveu Quantum Criticality in Twisted Bilayer Graphene: A Quantum Monte Carlo Study
• Fermi-liquid ground state of interacting Dirac fermions in two dimensions
• Stability of zero energy Dirac touchings in the honeycomb Hofstadter problem
• Soluble Fermionic Quantum Critical Point in Two Dimensions
• Generalized dynamical mean-field theory of two-subalttice systems with non-local interactions and its application to study charge and spin correlations in graphene
• Fermionic Sign Problem Minimization by Constant Path Integral Contour Shifts
• Mitigating spikes in fermion Monte Carlo methods by reshuffling measurements
• SO(4) multicriticality of two-dimensional Dirac fermions
• Magnetic, charge, and transport properties of graphene nanoflakes
• Mixed temperature-dependent order parameters in the extended Hubbard model
• Spectral functions of the honeycomb lattice with both the Hubbard and long-range Coulomb Interactions
• Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions
• Link auxiliary field method in the Extended Hubbard model
• Quantum phase transitions on the hexagonal lattice
• Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides
• Cuprates and center vortices: A QCD confinement mechanism in a high-Tc context
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