Impact of Quenched Disorders on The Holstein Model*

Over the last few decades, there has been considerable interest in the effects of disorder on the competition between superconductivity and
charge order wave (CDW) in underdoped cuprates. Similar questions arise in the study of the interplay of polaron formation and ordering with Anderson localization in disordered electron-phonon systems such as superconducting peroskites, and colossal magnetoresistance manganites. Many interesting phenomena are observed including non-Fermi liquid behavior and metal-insulator transitions (MIT) due to the opening of a CDW gap or due to Anderson localization. The combination of electron-phonon coupling and randomness leads to rich phase regimes as the phonon frequency ω, electron-phonon coupling λ and disorder strength △ vary. Here we present results from the DQMC method for the two-dimensional disordered Holstein model. We focus on the dependence of sizes of domain walls as well as the correlation length of density fluctuations. We also show the results for the temperature dependence of the conductance and compare to existing dynamical mean field theory results.