Given a model Hamiltonian for strongly correlated electrons, several key questions arise: What are the emergent energy scales? How should we characterize the resulting phases? And how can we understand the various quantum phase transitions that may occur? Unbiased numerical methods play a central role in this endeavor, as they guide us toward the correct emergent low‑energy field theories. In this colloquium, after a general introduction, I will focus on models of heavy‑fermion systems, which are most naturally understood from the perspective of a compact U(1) gauge theory. In particular, I will show that spin chains on metallic and semimetallic surfaces have the potential to realize the standard phases of heavy fermions, including Kondo‑breakdown transitions as well as magnetic order–disorder transitions in metallic environments.

This lecture was made possible by the William C. Ferguson Fund.