ICMT - Theory Seminar - 3/31/25 - Yueqing Chang

Abstract:

Ab-initio downfolding, which aims to bridge the ab-initio and model worlds, typically involves two key steps: truncation of the Hilbert space and matching of either the energy spectrum or the interaction parameters. Despite its widespread use, the standard downfolding methods contain approximations that remain largely unexplored, leading to limited a priori knowledge about the performance of the downfolded model. In this talk, I will first present a comprehensive benchmark of the standard downfolding techniques with the best-possible quantum chemistry results for a molecular test system, where our findings reveal the relative importance of each downfolding step and offer insights into the potential accuracy of the state-of-the-art downfolding methods. 

In the second part of the talk, I will introduce a framework for deriving systematically improvable interacting models using ab-initio data, focusing on the matching of many-body states. I will demonstrate its applications in deriving spin models for hydrogen chains and an Anderson impurity model for twisted bilayer graphene (TBG) with vacancies. Specifically, I will show how ab-initio downfolding for TBG+vacancy reveals a clear dichotomy in the Kondo energy scales between vacancies in AA/BB and AB/BA regions, which could be used as an experimental probe of both the critical single-particle states and the multifractal structure of the many-body ground state in magic-angle TBG.