Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions

Abstract

Quantum critical phenomena may be qualitatively different when massless Dirac fermions are present at criticality. Using our recently-discovered fermion-sign-free Majorana quantum Monte Carlo (MQMC) method introduced by us in Ref. [1], we investigate the quantum critical phenomena of {\it spinless} Dirac fermions at their charge-density-wave (CDW) phase transitions on the honeycomb lattice having $N_s=2L^2$ sites with largest $L=24$. By finite-size scaling, we accurately obtain critical exponents of this so-called Gross-Neveu chiral-Ising universality class of {\it two} (two-component) Dirac fermions in 2+1D: $\eta =0.45(2)$, $\nu =0.77(3)$, and $\beta =0.60(3)$, which are qualitatively different from the mean-field results but are reasonably close to the ones obtained from renormalization group calculations.

5.3 pages, Published as part of "Focus on Topological Physics: From Condensed Matter to Cold Atoms and Optics" in New Journal of Physics

References in corpus (18)

• The electronic properties of graphene
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Topological Mott Insulators
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Interactions and phase transitions on graphene's honeycomb lattice
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• 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
• Solving fermion sign problem in quantum Monte Carlo by Majorana representation
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Emergent space-time supersymmetry in 3D Weyl and 2D Dirac semimetals
• Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Theory of the nodal nematic quantum phase transition in superconductors
• Solution to sign problems in half-filled spin-polarized electronic systems
• Search for Neutrinoless Double-Beta Decay of ${}^{100}$Mo with the NEMO-3 Detector
• Efficient continuous-time quantum Monte Carlo algorithm for fermionic lattice models
• Current Carrying Ground State in a Bi-layer Model

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