Numerical investigations of Holstein phonons on the periodic Anderson model

Abstract

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 first 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 mean-field theory, where interaction expansion continuous time quantum Monte Carlo is used as impurity solver. The introduction of dynamical mean-field 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 mean-field theory simulation by solving a single site problem. In the infinite coordinate number limit, the dynamical mean-field 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 effect of phonon coupling to the conduction band of the periodic Anderson model is discussed. In the periodic Anderson model at low temperature region, the local moments on f -band are screened by the conduction electrons and form the coherent Kondo singlet states. When the lattice oscillation degree of freedom is introduced to the conduction band, the conduction electrons bond with each other because of the retarded attractive interaction incurred by the phonons. As the electron-phonon interaction is large, the competition of electronic bonding on the c -band will compete with the Kondo singlet bonding between the conduction electrons and the local moments and finally lead to a Kondo collapse. In the fourth 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