Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions
arxiv(2024)
摘要
Two-particle response functions are a centerpiece of both experimental and
theoretical quantum many-body physics. Yet, due to their size and discontinuity
structure, they are challenging to handle numerically. Recently, two advances
were made to tackle this problem: first, the overcomplete intermediate
representation (OIR), which provides a highly efficient compression of Green's
functions in imaginary frequency, and second, partial spectral functions
(PSFs), which allow for an efficient evaluation in real frequency. We show that
there is a two-to-one correspondence between PSFs and OIR coefficients and
exploit this fact to construct the OIR for three-or-more-particle propagators.
We then use OIR to fit and compress imaginary-frequency data obtained from the
numerical renormalization group (NRG), reaching a compression ratio of more
than 400. Finally, we attempt to match the OIR data to partial Green's
functions from NRG.Due to the overcompleteness, we achieve only qualitative
agreement.
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