We study the effects of anharmonicity on the physics of the Holstein model, which describes the coupling of itinerant fermions and localized quantum phonons, by introducing a quartic term in the phonon potential energy. We find that the presence of t
his anharmonic term reduces the extent of the charge density wave phase (CDW) at half-filling as well as the transition temperature to this phase. Doping away from half-filling, we observe a first order phase transition between the CDW and a homogeneous phase which is also present in the harmonic model. In addition, we study the evolution of the superconducting susceptibility in the doped region and show that anharmonicity can enhance the superconducting response.
Over the past several years, reliable Quantum Monte Carlo results for the charge density wave transition temperature $T_{cdw}$ of the half-filled two dimensional Holstein model in square and honeycomb lattices have become available for the first time
. Exploiting the further development of numerical methodology, here we present results in three dimensions, which are made possible through the use of Langevin evolution of the quantum phonon degrees of freedom. In addition to determining $T_{cdw}$ from the scaling of the charge correlations, we also examine the nature of charge order at general wave vectors for different temperatures, couplings, and phonon frequencies, and the behavior of the spectral function and specific heat.
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 CDW transition temperature is relatively insensitive to moderate anisotropy $delta lesssim 0.3$, but begins to decrease more rapidly at $delta gtrsim 0.4$. However, the density correlations, as well as the kinetic energies parallel and perpendicular to the compressional axis, change significantly for moderate $delta$. Accompanying mean-field theory calculations show a similar qualitative structure, with the transition temperature relatively constant at small $delta$ and a more rapid decrease for larger strains. We also obtain the density of states $N(omega)$, which provides clear signal of the charge ordering transition at large strain, where finite size scaling of the charge structure factor is extremely difficult because of the small value of the order parameter.
