Beyond quantum cluster theories: multiscale approaches for strongly 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.

Superfluid Mott-insulator quantum phase transition in an open cavity optomagnonic system

“…Quantum simulation provides a useful tool to explore new phenomena in quantum strongly correlated systems [1][2][3][4][5], exciton-polariton condensates [6][7][8], and high-temperature superconductivity [9][10][11]. Due to the controllability and compatility of atomic and optical systems, coupled cavity array is an promising and widely accepted system for quantum simulations.…”

Non-Fermi Liquid Behavior in the Three-Dimensional Hubbard Model

“…In this appendix, we provide a brief overview of the dynamical cluster approxiamtion (DCA) used in this paper. Additional details can be found in the original paper [38] or in several reviews on quantum cluster methods [39,54,55]. The DCA is an extension of the dynamical mean field theory (DMFT).…”

“…We can extract the self-energy by inverting the Dyson equation. With the self-energy, the process is then repeated until the self-energy is converged [39,54,55].…”