UC Davis

Electron-phonon interactions play an important role in understanding the properties of many materials, and give rise to the non-trivial correlation effects, explaining the emergence of a variety of ordered phases. This dissertation presents a Hybrid Quantum Monte Carlo (HQMC) method for simulating quantum electron-phonon models. The details of this approach are explained within the context of applying it to the widely studied Holstein model. We show that by achieving a computational cost that scales near linearly with lattice size, HQMC enables the simulation of system sizes a full order of magnitude larger than previously possible. Moreover, by using intelligently constructed global updates that significantly reduce autocorrelation times, we are able to simulate models with phonon frequencies in the adiabatic limit that are physically relevant to real materials. We then study the emergence of Charge Density Wave (CDW) order in several distinct Holstein models. The first includes electron hoppings (kinetic energies), which are different in the x and y directions, describing a lattice to which strain has been applied. We also extend previous investigations of CDW order in the square Holstein model to a cubic lattice,providing the first determination of the critical temperature in three dimensions.