Simon Friederich Knihy

Focusing on the two-dimensional Hubbard model, this work explores the interactions of fermions on a square lattice to understand Cooper pair formation in high-Tc cuprates. Utilizing functional renormalization group techniques, it introduces bosonic fields linked to various collective orders such as magnetism and superconductivity. Through "flowing bosonization," the study efficiently parameterizes the effective interactions, enabling the analysis of renormalization flow in symmetry-broken regimes. The findings include a detailed phase diagram showcasing the interplay between competing orders.

This Element focuses on the circumstances in which the restriction of gauge theories to gauge invariant information on an observable level is warranted, using the Brout-Englert-Higgs theory as an example of particular current importance.