Vertex corrections in strongly correlated electron systems : timescales of the spin and charge response

Abstract

Strongly correlated electron systems show some of the most intriguing phenomena in condensed matter physics. They range from high-temperature superconductivity in cuprates (presumably due to anti-ferromagnetic spin fluctuations) via new quasi-particles like the pi-tons to impact ionization in solar cells (which may be utilized to overcome the Shockley-Queisser limit on the efficiency of solar cells). None of these phenomena can be fully understood without considering the strong interactions (or correlations) between electrons in these quantum many-body systems. Mathematically, the many-body aspects of these problems can be described through vertex corrections. This thesis is dedicated to the following research question: “To what extent are vertex corrections important for the timescales of the spin and charge response?” To answer this question, the spin-spin and current-current correlation functions are examined in several different studies of the Hubbard model.The first study investigates the spin susceptibility for the dynamical mean-field theory solution (exact in the limit of infinite dimensions or coordination number) to the single-orbital Hubbard model. The results show an onset of asymptotic temporal magnetic correlations for a particular parameter regime. An algorithmic procedure to reliably extract this long-term memory feature from imaginary-time quantum Monte Carlo data is devised.Another study is devoted to the effect of strong anti-ferromagnetic fluctuations on the optical conductivity. In the metallic regime, the primary effect of the corresponding vertex correction in the ph-channel – called π-ton – can also be captured by a simplified semi-analytical diagrammatic calculation. Evaluating the corresponding Feynman diagrams shows a temperature-dependent broadening and sharpening of the Drude peak. In the last set of studies, photoexcitations in small Hubbard clusters are investigated. In particular, the phenomenon of impact ionization after irradiation with a (classically treated) light pulse is examined with time-resolved exact diagonalization. As a tool to better analyze the out-of-equilibrium dynamics, a generalization to the Loschmidt amplitude is proposed.This way, one can resolve which many-body energy eigenstates are responsible for impact ionization. Furthermore, it is demonstrated that the major effect of vertex corrections to the optical absorption in these particular Hubbard clusters is on the peak structure. The band gap, on the other hand, remains almost unchanged.