Reviews of topical problems

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

  a, b,   a, c, §  a, c
a International Center for Quantum Optics and Quantum Technologies (the Russian Quantum Center), ul. Novaya 100, Skolkovo, Moscow Region, 143025, Russian Federation
b National Research Nuclear University ‘MEPhI’, Kashirskoe shosse 31, Moscow, 115409, Russian Federation
c Lomonosov 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.

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Fulltext is also available at DOI: 10.3367/UFNe.2022.09.039231
Keywords: strongly correlated systems, dynamical mean-field theory, fluctuations
PACS: 71.10.−w
DOI: 10.3367/UFNe.2022.09.039231
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
PT Journal Article
TI Mean-field concept and post-DMFT methods in the modern theory of correlated systems
AU Lyakhova Ya S
FAU Lyakhova YS
AU Astretsov G V
FAU Astretsov GV
AU Rubtsov A N
FAU Rubtsov AN
DP 10 Aug, 2023
TA Phys. Usp.
VI 66
IP 8
PG 775-793
RX 10.3367/UFNe.2022.09.039231
SO Phys. Usp. 2023 Aug 10;66(8):775-793

Received: 14th, March 2022, revised: 6th, September 2022, 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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