Effective Models for Dynamically Screened Interactions

Sammanfattning

This master’s thesis project explores different methods for determining an effective electron-electron interaction strength to model dynamic interactions in the Anderson impurity model, an important model within the field of many-body quantum mechanics. The Anderson model describes an impurity atom which is embedded in a metal, with which in can exchange electrons. In this project, different observables for the dynamic Anderson model are estimated using continuous time quantum Monte Carlo simulations, and values for the imaginary time Green’s function are then used to develop various methods for obtaining the effective interaction strength. The main methods explored are neural networks and Bayesian parameter estimation. The accuracy of these effective models is evaluated by comparing their predictions of other observables, such as the double occupancy density and the kinetic energy. The results indicate that several of these methods could be utilized to make accurate predictions within certain domains of parameter space. The predictions made by the neural network and Bayesian inference methods were deemed to have a similar accuracy, which varied slightly for different temperatures.