  Precise algorithms capable of providing controlled solutions in the presence
of strong interactions are transforming the landscape of quantum many-body
physics. Particularly exciting breakthroughs are enabling the computation of
non-zero temperature correlation functions. However, computational challenges
arise due to constraints in resources and memory limitations, especially in
scenarios involving complex Green's functions and lattice effects. Leveraging
the principles of signal processing and data compression, this paper explores
the wavelet decomposition as a versatile and efficient method for obtaining
compact and resource-efficient representations of the many-body theory of
interacting systems. The effectiveness of the wavelet decomposition is
illustrated through its application to the representation of generalized
susceptibilities and self-energies in a prototypical interacting fermionic
system, namely the Hubbard model at half-filling in its atomic limit. These
results are the first proof-of-principle application of the wavelet compression
within the realm of many-body physics and demonstrate the potential of this
wavelet-based compression scheme for understanding the physics of correlated
electron systems.
