Low-Scaling Many-Body Perturbation Theory for Nanoscopic Systems

We present a low-scaling diagrammatic Monte Carlo approach to molecular correlation energies. Using combinatorial graph theory to encode many-body Hugenholtz diagrams, we sample the M\o{}ller-Plesset ( $\mathrm{MP}n$ ) perturbation series, obtaining accurate correlation energies up to $n=5$ , with quadratic scaling in the number of basis functions. Our technique reduces the computational complexity of the molecular many-fermion correlation problem, opening up the possibility of low-scaling, accurate stochastic computations for a wide class of many-body systems described by Hugenholtz diagrams.We present a low-scaling diagrammatic Monte Carlo approach to molecular correlation energies. Using combinatorial graph theory to encode many-body Hugenholtz diagrams, we sample the M\o{}ller-Plesset ($\mathrm{MP}n$) perturbation series, obtaining accurate correlation energies up to $n=5$, with quadratic scaling in the number of basis functions. Our technique reduces the computational complexity of the molecular many-fermion correlation problem, opening up the possibility of low-scaling, accurate stochastic computations for a wide class of many-body systems described by Hugenholtz diagrams.

arXiv:2203.12666Physical review. B./Physical review. BJul 11, 20231 citation

ASPECTS OF MANY-BODY PERTURBATION THEORY

WORLD SCIENTIFIC eBooksFeb 19, 20190 citations

Correlation effects in transport properties of interacting nanostructures

Angelo Valli, Giorgio Sangiovanni, A. Toschi +1 more

We discuss how to apply many-body methods to correlated nanoscopic systems, and provide general criteria of validity for a treatment at the dynamical mean field theory (DMFT) approximation level, in which local correlations are taken into account, while nonlocal ones are neglected. In this respect, we consider one of the most difficult cases for DMFT, namely, for a quasi-one-dimensional molecule such as a benzene ring. The comparison against a numerically exact solution shows that nonlocal spatial correlations are relevant only in the limit of weak coupling between the molecule and the metallic leads and of low inter-atomic connectivity, otherwise DMFT provides a quantitative description of the system. As an application we investigate the role of correlations on electronic transport in quantum junctions, and we show that a local Mott-Hubbard crossover is a robust phenomenon in sharp nanoscopic contacts.We discuss how to apply many-body methods to correlated nanoscopic systems, and provide general criteria of validity for a treatment at the dynamical mean field theory (DMFT) approximation level, in which local correlations are taken into account, while nonlocal ones are neglected. In this respect, we consider one of the most difficult cases for DMFT, namely, for a quasi-one-dimensional molecule such as a benzene ring. The comparison against a numerically exact solution shows that nonlocal spatial correlations are relevant only in the limit of weak coupling between the molecule and the metallic leads and of low inter-atomic connectivity, otherwise DMFT provides a quantitative description of the system. As an application we investigate the role of correlations on electronic transport in quantum junctions, and we show that a local Mott-Hubbard crossover is a robust phenomenon in sharp nanoscopic contacts.

arXiv:1309.3477Physical Review BSep 14, 201229 citations

Large Scale Many-Body Perturbation Theory calculations: methodological developments, data collections, validation

Marco Govoni, Giulia Galli

Bulletin of the American Physical SocietyMar 14, 20170 citations

Many Body Perturbation Theory for Non-Uniform Electronic Systems

D. F. Scofield

Springer eBooksJan 1, 19740 citations

\mathrm{MP}n

) perturbation series, obtaining accurate correlation energies up to

n=5

, with quadratic scaling in the number of basis functions. Our technique reduces the computational complexity of the molecular many-fermion correlation problem, opening up the possibility of low-scaling, accurate stochastic computations for a wide class of many-body systems described by Hugenholtz diagrams.