Numerical Investigations of Holstein Phonons on the Periodic Anderson Model

In condensed matter physics, the idea of localized magnetic moments and the scattering of conduction electrons by those local moments are of central importance not only for explaining the transport of electrons at low temperature region but also for developing the related models and theories to extend our understanding of novel physics like non-conventional superconductor, quantum phase transition and non-Fermi liquid behavior. In the rst chapter of this work, I will look back at the discovery of Kondo scattering, the introduction of Anderson impurity scenario, the extension to lattice version of the Anderson impurities, the periodic Anderson model, and how these ideas are used to the heavy fermion materials. In order to attack those problems and models numerically, in the second chapter, I will discuss the algorithm of dynamical meaneld theory, where interaction expansion continuous time quantum Monte Carlo is used as impurity solver. The introduction of dynamical meaneld theory and its related methods are one of the largest victory of computational condensed matter physics in the past three decades. By mapping the lattice problem to an impurity problem and solving it self-consistently, we can get the static and dynamic outputs in the thermal dynamical limit from dynamical meaneld theory simulation by solving a single site problem. In the in nite coordinate number limit, the dynamical meaneld theory results converge to the exact results. Quantum Monte Carlo is widely used in computational physics. Compared with the conventional quantum Monte Carlo, the recently introduced interaction expansion continuous time quantum Monte Carlo is free of decomposition error in imaginary time. In the third chapter, the pressure induced volume collapse problem of Cerium is explored. It has been discovered that Cerium will experience a 15% volume collapse from a large volume γ phase to a small volume α phase as the external pressure is above a certain critical value. Such fcc→ fcc iso-structure rst-order phase transition has long been thought to be driven by purely electronic factors but there are recent experimental evidences indicating that lattice oscillation contribute a tremendous part (20%~50%) of the entropy change in such rstorder phase transition. Using the periodic Anderson model with Holstein phonons on the conduction band, we found that only above a critical value of electron-phonon coupling such a model will experience a rst-order phase transition. As the external pressure is increased, consequently the hybridization between conduction and localized electrons is increased as well, and the system will be driven from a local moment+bipolaron phase to a Kondo singlet+polaron phase. In the pressure-temperature plain, the rst-order phase transition line which separates the local moment+bipolaron phase and the Kondo singlet+polaron phase terminates at a second order critical point. We hope our discovery may shed light on exploring the role of phonon degree of freedom in the long lasting Cerium volume collapse problem. In the appendix, the numerical details of the interaction expansion continuous time quantum Monte Carlo method are covered. The measurement of singlet particle and two particle Green's function, the numerical tricks in accomplishing better Fourier transformation results