We briefly review methods for modeling correlated systems. The concept of correlations is of fundamental physical importance for systems such as Mott—Hubbard insulators, high-temperature superconductors, molecular magnets, and twisted bilayer graphene. With the Hubbard model chosen as a reference, we systematically describe various numerical methods, starting with the mean-field and related theories that map the physical system under study onto an effective interaction-free ensemble. We also discuss the dynamical mean-field theory (DMFT), which is one of the most common modern methods to describe local correlations exactly. DMFT-based diagram methods incorporate effects of nonlocal physics to varying degrees, with the local correlations taken into account in full. In addition, we describe the nondiagram fluctuating local field method, whereby fluctuations of the leading collective modes of the system can be treated nonperturbatively.

Keywords: strongly correlated systems, dynamical mean-field theory, fluctuations PACS: 71.10.−w DOI: 10.3367/UFNe.2022.09.039231 URL: https://ufn.ru/en/articles/2023/8/b/ 001112646900002 2-s2.0-85163322735 2023PhyU...66..775L Citation: Lyakhova Ya S, Astretsov G V, Rubtsov A N "Mean-field concept and post-DMFT methods in the modern theory of correlated systems" Phys. Usp. 66 775–793 (2023) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 14th, March 2022, revised: 6th, September 2022, accepted: 7th, September 2022 Оригинал: Ляхова Я С, Астрецов Г В, Рубцов А Н «Концепция среднего поля и методы пост-DMFT в современной теории коррелированных систем» УФН 193 825–844 (2023); DOI: 10.3367/UFNr.2022.09.039231