Renormalization group for metals

Abstract: Metal such as Fermi liquid is one of the most prevalent phases of matter that we encounter in many quantum materials as well as our daily life. One important feature of Fermi liquid (and metal more generally) is the infinite number of zero modes on the fermi surface, which raises the question about whether the powerful theoretical tool--renormalization group (RG) is still applicable. In this talk I will present our recent work that develops the RG framework adapted to metals. Specifically, we considered the RG flow of coupling functions, and used it to study the complete low energy dynamics of Fermi liquid. Within this new framework, we can understand how Fermi liquid emerges or gets destroyed, e.g. by Pomeranchuk instability. Our work provides a general way to study the low energy physics of metals, and opens a new route to the system with an intrinsic scale from the perspective of RG.