Mean-field concept and post-DMFT methods in the modern theory of correlated systems

Ya.S. Lyakhova^†^a, b, G.V. Astretsov^‡^a, c, A.N. Rubtsov^§^a, c
^aInternational Center for Quantum Optics and Quantum Technologies (the Russian Quantum Center), Skolkovo Innovation Center, Bolshoi Boulevard, Building 30, Block 1, 3rd floor, sectors G3, G7, Moscow, Moscow Region, 121205, Russian Federation
^bNational Research Nuclear University ‘MEPhI’, Kashirskoe shosse 31, Moscow, 115409, Russian Federation
^cLomonosov Moscow State University, Vorobevy Gory, Moscow, 119991, Russian Federation

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/
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001112646900002
Scopus

2-s2.0-85163322735
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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)

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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

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