Numerical evidence of conformal phase transition in graphene with long-range interactions

Abstract

Using state of the art 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 suspended graphene. We determine that the realistic inter-electron potential of graphene must be scaled up by a factor of roughly 1.6 to induce a semimetal-SDW phase transition and find no evidence for CDW order. A study of critical properties suggests that the universality class of the three-dimensional chiral Heisenberg Gross-Neveu model with two fermion flavors, predicted by renormalization group studies and strong-coupling expansion, is unlikely to apply to this transition. We propose that our results instead favor an interpretation in terms of a conformal phase transition. In addition, we describe a variant of the HMC algorithm which uses exact fermionic forces during molecular dynamics trajectories and avoids the use of pseudofermions. Compared to standard HMC this allows for a substantial increase of the integrator stepsize while achieving comparable Metropolis acceptance rates and leads to a sizable performance improvement.

revised version, accepted for publication in Phys. Rev. B

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• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Simulating both parity sectors of the Hubbard Model with Tensor Networks
• 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
• Fermionic Sign Problem Minimization by Constant Path Integral Contour Shifts
• Generalized dynamical mean-field theory of two-subalttice systems with non-local interactions and its application to study charge and spin correlations in graphene
• Mitigating spikes in fermion Monte Carlo methods by reshuffling measurements
• Magnetic, charge, and transport properties of graphene nanoflakes
• Quantum Monte Carlo Study of Semiconductor Artificial Graphene Nanostructures
• Spectral functions of the honeycomb lattice with both the Hubbard and long-range Coulomb Interactions
• Instanton gas approach to the Hubbard model
• Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions
• Reduced QED with few planes and fermion gap generation
• Link auxiliary field method in the Extended Hubbard model
• Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides
• Quantum phase transitions on the hexagonal lattice
• The Semimetal-Antiferromagnetic Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice
• Fully ergodic simulations using radial updates
• Bridging the gap between numerics and experiment in free standing graphene
• The Hubbard model with fermionic tensor networks
• Lattice Field Theory Analysis of the Chiral Heisenberg Model