Langevin Simulations of the Half-Filled Cubic Holstein Model

Abstract

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.

Superconductivity and charge density wave order in the 2D Holstein model

“…Since our estimates of T sc lie below this upper bound, this suggests it may be possible to increase the transition temperature by increasing λ D . Recently, a QMC method based on Langevin updates of the phonon degrees of freedom [53,54] has also made studies of the cubic Holstein model amenable to simulation, and it has been found that T cdw at half-filling is increased roughly by a factor of two compared to various two-dimensional geometries [55]. We anticipate that in future studies of the 3D Holstein model one might similarly expect higher values of T sc away from half-filling, since the model will exhibit a more robust transition to long-ranged superconducting order, in contrast with the KT transition in two dimensions observed in this work.…”