Cross-extrapolation reconstruction of low-rank functions and application to quantum many-body observables in the strong coupling regime
arxiv(2024)
摘要
We present a general-purpose algorithm to extrapolate a low rank function of
two variables from a small domain to a larger one. It is based on the
cross-interpolation formula. We apply it to reconstruct physical quantities in
some quantum many-body perturbative expansions in the real time Keldysh
formalism, considered as a function of time t and interaction U. These
functions are of remarkably low rank. This property, combined with the
convergence of the perturbative expansion in U both at finite t (for any
U), and small U (for any t), is sufficient for our algorithm to
reconstruct the physical quantity at long time, strong coupling regime. Our
method constitutes an alternative to standard resummation techniques in
perturbative methods, such as diagrammatic Quantum Monte Carlo. We benchmark it
on the single impurity Anderson model and show that it is successful even in
some regime where standard conformal mapping resummation techniques fail.
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