Beyond Quantum Cluster Theories: Multiscale Approaches for Strongly Correlated Systems

TL;DR

This paper reviews multiscale many-body approaches that bridge short and long-range correlations in strongly correlated systems, overcoming computational limitations of traditional methods like DMFT and DCA.

Contribution

It introduces and discusses various multiscale methods that incorporate an intermediate length scale to improve treatment of correlations in strongly correlated materials.

Findings

Multiscale approaches effectively handle larger correlation lengths.

They overcome limitations of QMC and ED methods.

Promising results in modeling complex correlated systems.

Abstract

The degrees of freedom that confer to strongly correlated systems their many intriguing properties also render them fairly intractable through typical perturbative treatments. For this reason, the mechanisms responsible for these technologically promising properties remain mostly elusive. Computational approaches have played a major role in efforts to fill this void. In particular, dynamical mean field theory (DMFT) and its cluster extension, the dynamical cluster approximation (DCA) have allowed significant progress. However, despite all the insightful results of these embedding schemes, computational constraints, such as the minus sign problem in Quantum Monte Carlo (QMC), and the exponential growth of the Hilbert space in exact diagonalization (ED) methods, still limit the length scale within which correlations can be treated exactly in the formalism. A recent advance to overcome these difficulties is the development of multiscale many body approaches whereby this challenge is addressed by introducing an intermediate length scale between the short length scale where correlations are treated exactly using a cluster solver such QMC or ED, and the long length scale where correlations are treated in a mean field manner. At this intermediate length scale correlations can be treated perturbatively. This is the essence of multiscale many-body methods. We will review various implementations of these multiscale many-body approaches, the results they have produced, and the outstanding challenges that should be addressed for further advances.