Electronic structure involves a basic science study of the electronic excitations in molecular and nanostructured systems with significant technological implications. The role of theory in this field is to predict properties of materials as well as nanostructured and supramolecular systems. Hence the main challenges facing electronic structure theory are: predictive power and applicability for large systems. Predictivity implies the development of first-principles high-level treatments of electron correlations while tackling large systems requires low computational complexity. Progress is slow since these two requirements are mutually exclusive: high-level theories of electron correlation involve high computational complexity.[Whitfield2013]

In the past two decades approaches for low-scaling ab initio methods, based on density functional theory and perturbation theory, have been developed with varying degree of generality and success.[Goedecker1999, Gillan2007, Beer2008] However, unlike the quantum Monte Carlo methods for quantum chemistry, stochastic methods for electronic structure have not yet found a central role in the field. This situation is now changing as a surge of new ideas concerning stochastic quantum processes is observed. The proposed workshop is intended to bring together researchers that are developing new stochastic methods or low scaling high precision methods for electronic structure of large systems. The basic hope is that such a workshop can synergistically inspire researchers to develop new ideas and paradigms which can be used

Stochastic methods involve, necessarily, a stochastic process that allows efficient sampling of the configurational space from which the computed quantity can be estimated. The best known methods, such as variational, diffusion and Green's function Monte Carlo have already proved strengths and (unavoidably) weaknesses.[#Nightingale1999, #Hammond1994, #Gubernatis2016] Many workshops and schools on QMC methods are held annually and it is not our goal to entertain an additional meeting on this topic. Instead we aim at stochastic methods for the community developing techniques for accelerating the calculation of approximate (but highly accurate) electron correlation theories.

Such stochastic methods concerning electron correlation have recently been published, such as the stochastic CI [#Booth2009, #Ten-no2013, #Thomas2015], stochastic DFT,[#Baer2013, #Neuhauser2015], coupled-cluster and perturbation theory [#Thom2010, #Thom2007a, #Willow2012, #Neuhauser2013], random phase approximation,[#Neuhauser2013a] GW theory[#Neuhauser2014], response and Bethe-Salpeter equation,[#Neuscamman2013, #Rabani2015], theory of multiexciton generation rates in nanocrystals.[#Baer2012a] and continuous time Monte Carlo for nonequilibrium quantum impurity problems.[#Muehlbacher2008, #Gull2011, #Cohen2015]

The aim of the proposed workshop is to bring together the leading scientists representing low complexity and/or stochastic approaches for large scale electronic structure calculations. Unlike workshops on Quantum Monte Carlo methods focusing on the solution of the many-body Schrödinger equation, the proposed workshop targets stochastic approaches to high complexity single- or two-particle methods such as 1) for ground states: density functional and Hartree-Fock (DFT and HFT) theory, perturbative methods (Random Phase Approximation (RPA), Moller-Plesset Theory MPn, coupled cluster (CC) approaches), geminal electronic structure and 2) for excitations response and dynamics: many-body perturbation theory (GW, Bethe-Salpeter GF2, time-dependent DFT (TDDFT) etc.) and continuous time Monet Carlo.

The idea behind the proposed workshop is to bring together experts developing a wide range of tools to solve the quantum many-body problem. The unifying theme is the stochastic nature of the algorithms underlying the approaches developed by the invited speakers. The workshop will include experts that rarely meet and discuss science. This unique environment will provide scientists additional tools to expand into novel directions by adopting approaches from other fields. All invited speakers are leaders in the field of the quantum many-body problem and have contributed to the development of methods and applications in one of the fields, i.e. density function theory and its time dependent version, perturbative electronic structure methods, many-body perturbation techniques, and many-body diagrammatic methods. The diverse background of speaker’s expertise in method development and applications is expected to lead to synergetic collaborations of researchers from different disciplines, all working on the quantum many-body problem..

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