Langevin Simulation of Half-filled Cubic Holstein Model

Over the past several years, reliable Quantum Monte Carlo results for the charge density wave transition temperature Tcdw 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 Tcdw 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.