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The effect of electron-electron interactions on Dirac fermions, and the possibility of an intervening spin liquid phase between the semi-metal and antiferromagnetic (AF) regimes, has been a focus of intense quantum simulation effort over the last five years. We use determinant quantum Monte Carlo (DQMC) to study the Holstein model on a Honeycomb lattice and explore the role of electron-phonon interactions on Dirac fermions. We show that they give rise to charge density wave (CDW) order, and present evidence that this occurs only above a finite critical interaction strength. We evaluate the temperature for the transition into the CDW which, unlike the AF transition, can occur at finite values owing to the discrete nature of the broken symmetry.
We investigate charge ordering in the Holstein model in the presence of anisotropic hopping, $t_x, t_y=1-delta, 1 + delta$, as a model of the effect of strain on charge density wave (CDW) materials. Using Quantum Monte Carlo simulations, we show that
The Holstein Hamiltonian describes fermions hopping on a lattice and interacting locally with dispersionless phonon degrees of freedom. In the low density limit, dressed quasiparticles, polarons and bipolarons, propagate with an effective mass. At hi
We use an unbiased, continuous-time quantum Monte Carlo method to address the possibility of a zero-temperature phase without charge-density-wave (CDW) order in the Holstein and, by extension, the Holstein-Hubbard model on the half-filled square latt
We explore the possibility of inducing a topological insulator phase in a honeycomb lattice lacking spin-orbit interaction using a metallic (or Fermi gas) environment. The lattice and the metallic environment interact through a density-density intera
We consider the quasi-two-dimensional pseudo-spin-1/2 Kitaev - Heisenberg model proposed for A2IrO3 (A=Li, Na) compounds. The spin-wave excitation spectrum, the sublattice magnetization, and the transition temperatures are calculated in the random ph