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Molecular Physics

Bridging quantum chemistry and solid-state physics

So Hirata

Published Sep 18, 2010• 7 citations
Publisher

Abstract

This article reviews the developments made primarily by the author in mathematical theories and algorithms for systematic many-body descriptions of correlated electrons and anharmonic lattice vibrations in polymers and molecular crystals. It also documents underlying size-extensive electron-correlation methods and their computerized implementations as well as a few pivotal applications.

DOI
10.1080/00268976.2010.516278

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This article reviews the developments made primarily by the author in mathematical theories and algorithms for systematic many-body descriptions of correlated electrons and anharmonic lattice vibrations in polymers and molecular crystals. It also documents underlying size-extensive electron-correlation methods and their computerized implementations as well as a few pivotal applications.
The pursuit of accurate and computationally efficient many-body tools capable\nof describing electron correlation is a major effort of the quantum chemistry\ncommunity. The accuracy of chemical predictions strongly depends on the ability\nof the models to account for electron correlation. As the computational\ndemand scales unfavourably with the size of the system, an efficient way of\nidentifying relevant degrees of freedom may be an interesting avenue.\n\nIn this thesis, a quantum embedding approach is employed to study lattice\nsystems, polymers, and crystals. Numerical data shows the\naccuracy of the quantum embedding theory when combined with high-level\nmany-body techniques. As the size of the units that are embedded\ngrows, a more approximate and more computationally affordable\ntools are called for. In this thesis, we investigate the possibility of\nforming such methods in the framework of coupled cluster theory.\n\nWe believe that the tools presented in this thesis could be important\nfor accurate treatment of electron correlation in applications to\nrealistic materials.
There are a number of many-body systems which exhibit quantum effects on a macroscopic scale. These include liquid and crystal states of both He-3 and He-4, the electron gas, and neutron matter which probably constitutes the interior of pulsors. In addition, "nuclear matter" - a hypothetical extensive system of nucleons has been studied for the insight one may gain into the nature of finite nuclei. The theoretical studies of these systems have by now a long history, but are by no means concluded. In the last few years, significant advances have been made. This has come in part from the maturity of and gradual unification of many-body theory, in part from the development and application of powerful new expansion procedures, especially varieties of hypernetted-chain equations ( 1 ) and finally to the growing power of computer simulation methods for quantum systems. This article is intended as a review of some recent
Aimed at graduate students and researchers, this book covers the key aspects of the modern quantum theory of solids, including up-to-date ideas such as quantum fluctuations and strong electron correlations. It presents in the main concepts of the modern quantum theory of solids, as well as a general description of the essential theoretical methods required when working with these systems. Diverse topics such as general theory of phase transitions, harmonic and anharmonic lattices, Bose condensation and superfluidity, modern aspects of magnetism including resonating valence bonds, electrons in metals, and strong electron correlations are treated using unifying concepts of order and elementary excitations. The main theoretical tools used to treat these problems are introduced and explained in a simple way, and their applications are demonstrated through concrete examples.
The study of strongly correlated materials remains one of the most challenging and active frontiers in condensed matter physics. In these systems, the intricate interplay between electrons' kinetic energy and their mutual Coulomb repulsion gives rise to a plethora of exotic phenomena, from high-temperature superconductivity to giant magnetoresistance, which cannot be explained by conventional one-electron theories. This necessitates the development and application of advanced theoretical and computational methods capable of capturing the essential physics of strong electronic correlations. A diverse array of numerical and analytical techniques has been developed to tackle the many-body problem. However, no single method serves as a panacea; each comes with its own set of strengths and weaknesses, and their domains of applicability vary significantly. The choice of an appropriate approximation is therefore highly dependent on the specific physical system and the scientific question at hand. Different problems may benefit from different, and sometimes complementary, methodological perspectives. This thesis focuses primarily on the application and development of local or quasi-local approaches. The rationale for this focus is rooted in the physical reality of many key correlated materials, such as transition metal oxides, heavy-fermion systems or molecular solids like alkali-doped fullerenes, where the local on-site electronic interaction is the dominant energy scale. By prioritizing the accurate treatment of local physics, these methods provide a robust and computationally efficient approximation for understanding a wide range of material properties. Recent experimental and theoretical advancements—spanning the rich physics of multiorbital compounds, the precise control over interactions in ultracold atomic gases, and the complex interplay in electron-phonon coupled systems—have created an urgent need for theoretical frameworks that can deliver reliable and rapid insights. The methods explored in this work are meant to address these challenges, offering a balance between accuracy and computational feasibility. Given the variety of topics addressed, from methodological developments to their application in diverse physical contexts, this thesis will try to be as detailed and self-contained as necessary, providing a clear exposition of the underlying concepts and technical aspects.