Low-rank approximations have long been considered an efficient way to accelerate
electronic structure calculations associated with the evaluation of electron repulsion …

We review a suite of stochastic vector computational approaches for studying the electronic
structure of extended condensed matter systems. These techniques help reduce algorithmic …

Accurate description of nonadiabatic dynamics of molecules at metal surfaces involving
electron transfer has been a long-standing challenge for theory. Here, we tackle this …

This lecture note reviews recently proposed sparse-modeling approaches for efficient ab
initio many-body calculations based on the data compression of Green's functions. The …

We present a real-time second-order Green's function (GF) method for computing excited
states in molecules and nanostructures, with a computational scaling of O (N e3), where N e …

We explore the use of the stochastic resolution-of-the-identity (sRI) with the phaseless
auxiliary-field quantum Monte Carlo (ph-AFQMC) method. sRI is combined with four existing …

Wannier functions have become a powerful tool in the electronic structure calculations of
extended systems. The generalized Pipek-Mezey Wannier functions exhibit appealing …

We develop a stochastic resolution of identity approach to the real-time second-order
Green's function (real-time sRI-GF2) theory, extending our recent work for imaginary-time …

We apply a stochastic resolution of identity approximation (sRI) to the CC2 method for the
excitation energy calculations. A set of stochastic orbitals are employed to decouple the …

Stochastic orbital techniques offer reduced computational scaling and memory requirements
to describe ground and excited states at the cost of introducing controlled statistical errors …