Oleksandr Sulyma

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Quantum corrections in many-body physics and general quantum field theories are captured by renormalised interactions, or one-particle irreducible (1PI) vertices. Their complex frequency and momentum structure makes them challenging to treat numerically. In this talk, I present a unified framework based on the effective action for composite fields, which generalises several recent and practically useful decompositions of the 4-point vertex developed in the context of correlated electron systems. These include the frequency parametrisation using the asymptotic classes, the single-boson exchange decomposition to avoid vertex divergences that appear in the parquet formalism, and symmetric improved estimators that eliminate the need for Green’s function amputation. I demonstrate that these representations correspond to different choices of composite fields and naturally extend to more general theories and any-order vertices via simple tree diagrams. This suggests the possibility of new decompositions that could further simplify the numerical treatment of 1PI vertices.

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LMU München
0.03
Contact: Fabian Kugler