Non-perturbative methods for metallic quantum criticality and beyond

• Applicant: Dr. Dimitri Pimenov
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2020 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 442134789

Many fascinating phenomena in metallic materials are possibly connected to a "quantum phase transition" (QPT) at zero temperature. For example, the competition of different microscopical ordering tendencies near a QPT could be responsible for the mysterious vanishing resistance in high-temperature superconductors.The theoretical description of these QPTs is quite challenging due to strong interactions effects, and mostly relied on perturbative methods so far. That is, one introduces an artificial small parameter to render computations controlled. These methods have natural limitations, and might even lead to qualitatively wrong predictions.To make progress, I will contribute to the development of "non-peturbative" tools, with two points of attack: As a starting point, I will study a realistic model of a QPT in a metal, related to the onset of a density modulation. I will apply a novel analytical technique, entitled "interaction-driven scaling", which puts interaction effects in focus; as a result, an actual (non-artificial) small parameter should emerge, as indicated by my preliminary computations. This opens up the exciting prospect of solving the model exactly in the physically relevant limit of low energies. I will make predictions for experimental observables, and will also generalize the technique to other analytical applications. Second, I will explore the "interaction-driven scaling" in the context of the semi-numerical method "functional renormalization group" (fRG), which also does without an artificial small parameter. Furthermore, I plan the application of a recently developed extension called "multiloop fRG" , which is particularly suited to understand competing ordering tendencies in an unbiased fashion. By applying it to a simplified model of electrons known to host a QPT, I therefore hope to contribute to a better understanding of unconventional superconductivity.

• DFG Programme: Research Fellowships
• International Connection: USA
• Host: Professor Debanjan Chowdhury