%0 Generic
%A Wetzel, Sebastian Johann
%D 2018
%F heidok:25528
%R 10.11588/heidok.00025528
%T Exploring Phase Diagrams with Functional  Renormalization and Artificial Neural Networks:  From the Hubbard Model  to Lattice Gauge Theory
%U https://archiv.ub.uni-heidelberg.de/volltextserver/25528/
%X This thesis is dedicated to provide physicists with new and improved techniques to  examine phase diagrams and phase transitions.  One the one hand, an analysis of the effects of different regularization schemes in  functional renormalization group calculations is provided. Building on this knowledge,  an investigation of the phase diagram of the Hubbard-Model on the square  lattice is performed using the functional renormalization group. The calculation  reveals leading instabilities in the d-wave superconducting and different antiferromagnetic  channels. In the symmetry broken phases there are a changing Fermi  surface geometry, coexistence phases of d-wave superconductivity and antiferromagnetism  as well as a mutual tendency of superconductivity and antiferromagnetism  to repel each other.  On the other hand, a scheme to discover phase transitions using unsupervised  artifcial neural networks is developed. Further, a method to interpret artifcial  neural networks is introduced. These methods are applied to systems ranging from  the two dimensional Ising Model to four dimensional SU(2) lattice gauge theory.  They find the existence of different phases, calculate phase boundaries and derive  the explicit formulas of the quantities by which the neural network distinguishes  between phases. It turns out that these quantities are order parameters and other  thermodynamic quantities.