Solids with weak and strong electron correlations

TL;DR

This paper reviews methods for treating electron correlations in solids, distinguishing approaches for weakly and strongly correlated systems, and discusses phenomena like electron crystallization and heavy-fermion behavior.

Contribution

It compares computational techniques for weak and strong electron correlations and explores their applications to various complex solid-state phenomena.

Findings

Incremental quantum chemical methods yield high-quality results for weakly correlated solids.

Model Hamiltonians and projection techniques are effective for strongly correlated electron systems.

Different physical phenomena such as electron crystallization and heavy-fermion behavior are discussed in context.

Abstract

A number of methods are discussed which may serve for a treatment of electron correlations in solids. When the electron correlations are relatively weak like in semiconductors or a number of ionic crystals one may start from a self-consistent field calculation and include correlations by quantum chemical methods. An incremental computational scheme enables us to obtain results of high quality for the ground state of those systems. A number of examples demonstrates that explicitely. Solids with strongly correlated electrons require the use of model Hamiltonians. With their help one can tackle the problem of determining spectral densities for those systems. The projection technique is a useful tool here. In strongly correlated $f$ electron systems electron or holes can crystallize with quite different physical consequences as in the case of a Wigner crystal or Verwey transition. Finally, different routes to heavy-fermion behavior are discussed, another hallmark of strongly correlated electrons.