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/
Web of Science

001112646900002
Scopus

2-s2.0-85163322735
ADS NASA

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

References (186) Cited by (4) Similar articles (20) ↓

E.Z. Kuchinskii, I.A. Nekrasov, M.V. Sadovskii “Generalized dynamical mean-field theory in the physics of strongly correlated systems” Phys. Usp. 55 325–355 (2012)
V.V. Val’kov, D.M. Dzebisashvili et al “Spin-polaron concept in the theory of normal and superconducting states of cuprates” Phys. Usp. 64 641–670 (2021)
M.V. Sadovskii “High-temperature superconductivity in iron-based layered compounds” Phys. Usp. 51 1201–1227 (2008)
M.Yu. Kagan, V.A. Mitskan, M.M. Korovushkin “Anomalous superconductivity and superfluidity in repulsive fermion systems” Phys. Usp. 58 733–761 (2015)
Yu.S. Orlov, S.V. Nikolaev et al “Features of spin crossovers in magnetic materials” Phys. Usp. 66 647–672 (2023)
A.S. Mishchenko “Electron — phonon coupling in underdoped high-temperature superconductors” Phys. Usp. 52 1193–1212 (2009)
Yu.A. Izyumov “Hubbard model of strong correlations” Phys. Usp. 38 385–408 (1995)
S.I. Vedeneev “Pseudogap problem in high-temperature superconductors” Phys. Usp. 64 890–922 (2021)
V.Yu. Irkhin “Unusual magnetism of the Kondo lattice” Phys. Usp. 60 747–761 (2017)
M.F. Sarry “Analytical methods of calculating correlation functions in quantum statistical physics” Sov. Phys. Usp. 34 (11) 958–979 (1991)
A.V. Nikolaev, A.V. Tsvyashchenko “The puzzle of the γ→α and other phase transitions in cerium” Phys. Usp. 55 657–680 (2012)
B.M. Smirnov “Metal nanostructures: from clusters to nanocatalysis and sensors” Phys. Usp. 60 1236–1267 (2017)
N.A. Zimbovskaya “Local geometry of the Fermi surface and its effect on the electronic characteristics of normal metals” Phys. Usp. 54 769–798 (2011)
N.B. Ivanova, S.G. Ovchinnikov et al “Specific features of spin, charge, and orbital ordering in cobaltites” Phys. Usp. 52 789–810 (2009)
I.S. Lyubutin, A.G. Gavriliuk “Research on phase transformations in 3d-metal oxides at high and ultrahigh pressure: state of the art” Phys. Usp. 52 989–1017 (2009)
A.P. Protogenov “Anyon superconductivity in strongly-correlated spin systems” Sov. Phys. Usp. 35 (7) 535–571 (1992)
P.I. Arseev “On the nonequilibrium diagram technique: derivation, some features and applications” Phys. Usp. 58 1159–1205 (2015)
A.L. Ivanovskii “New high-temperature superconductors based on rare-earth and transition metal oxyarsenides and related phases: synthesis, properties, and simulations” Phys. Usp. 51 1229–1260 (2008)
R.O. Zaitsev, E.V. Kuz’min, S.G. Ovchinnikov “Fundamental ideas on metal-dielectric transitions in 3d-metal compounds” Sov. Phys. Usp. 29 322–342 (1986)
Yu.B. Kudasov “Short-range order in strongly correlated Fermi systems” Phys. Usp. 46 117–138 (2003)

The list is formed automatically.