SKM 2023 – wissenschaftliches Programm
DY 11: Focus Session: Physics Meets ML II – Understanding Machine Learning as Complex Interacting Systems (joint session DY/TT)
DY 11.8: Vortrag
Montag, 27. März 2023, 18:15–18:30, ZEU 250
Making machines untangle the parquet equations — •Samuel Badr1, Anna Kauch1, Hiroshi Shinaoka2, Karsten Held1, and Markus Wallerberger1 — 1TU Wien, Vienna, Austria — 2Saitama University, Saitama, Japan
Diagrammatic theories at the two-particle level are increasingly important in understanding the subtle interplay of phenomena occurring in strongly correlated electron systems. The parquet equations are a centerpiece of many such theories, since they are the simplest unbiased topological classification of two-particle diagrams. However, due to their eponymous interlocking structure, the parquet equations are vexingly difficult to solve, requiring prohibitive amounts of memory.
We tackle this problem using the recently developed, machine learning inspired, techniques: firstly, the overcomplete intermediate representation, a highly compressed model for two-particle objects which is guaranteed to converge exponentially; secondly, a sparse set of Matsubara frequencies tailored to the structure of the parquet equations. This allows us to perform convolutions and frequency shifts at no loss of accuracy.
We benchmark our solver for the Hubbard atom, where we reproduce analytic results, and then showcase the solver for more extended systems.