The correlation functions of quantum systems—central objects in quantum field theories—
are defined in high-dimensional space-time domains. Their numerical treatment thus suffers …

This review paper describes the basic concept and technical details of sparse modeling and
its applications to quantum many-body problems. Sparse modeling refers to methodologies …

Efficient ab initio calculations of correlated materials at finite temperatures require compact
representations of the Green's functions both in imaginary time and in Matsubara frequency …

Vertex functions are a crucial ingredient of several forefront many-body algorithms in
condensed matter physics. However, the full treatment of their frequency and momentum …

We present an efficient basis for imaginary time Green's functions based on a low-rank
decomposition of the spectral Lehmann representation. The basis functions are simply a set …

A major challenge in the field of correlated electrons is the computation of dynamical
correlation functions. For comparisons with experiment, one is interested in their real …

The parquet formalism and Hedin's GW γ approach are unified into a single theory of vertex
corrections, corresponding to an exact reformulation of the parquet equations in terms of …

The many-body problem is usually approached from one of two perspectives: the first
originates from an action and is based on Feynman diagrams, the second is centered …

We present a generalization of the discrete Lehmann representation (DLR) to three-point
correlation and vertex functions in imaginary time and Matsubara frequency. The …

The Bethe-Salpeter equation plays a crucial role in understanding the physics of correlated
fermions, relating to optical excitations in solids as well as resonances in high-energy …