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Journal ArticleDOI

Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory

TL;DR: In this paper, the authors present a review of the state-of-the-art methods for strong electronic correlations, starting with the local, eminently important correlations of dynamical mean field theory (DMFT).
Abstract: Strong electronic correlations pose one of the biggest challenges to solid state theory. We review recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field theory (DMFT). On top of this, non-local correlations on all length scales are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. With these diagrammatic extensions of DMFT long-range charge-, magnetic-, and superconducting fluctuations as well as (quantum) criticality can be addressed in strongly correlated electron systems. We provide an overview of the successes and results achieved---hitherto mainly for model Hamiltonians---and outline future prospects for realistic material calculations.
Citations
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Dissertation
01 Oct 1948
TL;DR: In this article, it was shown that a metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.
Abstract: IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

2,042 citations

Journal ArticleDOI
18 Mar 2020-Nature
TL;DR: A new solid-state platform based on moiré superlattices that can be used to simulate problems in strong-correlation physics that are described by triangular-lattice Hubbard models is established.
Abstract: The Hubbard model, formulated by physicist John Hubbard in the 1960s1, is a simple theoretical model of interacting quantum particles in a lattice. The model is thought to capture the essential physics of high-temperature superconductors, magnetic insulators and other complex quantum many-body ground states2,3. Although the Hubbard model provides a greatly simplified representation of most real materials, it is nevertheless difficult to solve accurately except in the one-dimensional case2,3. Therefore, the physical realization of the Hubbard model in two or three dimensions, which can act as an analogue quantum simulator (that is, it can mimic the model and simulate its phase diagram and dynamics4,5), has a vital role in solving the strong-correlation puzzle, namely, revealing the physics of a large number of strongly interacting quantum particles. Here we obtain the phase diagram of the two-dimensional triangular-lattice Hubbard model by studying angle-aligned WSe2/WS2 bilayers, which form moire superlattices6 because of the difference between the lattice constants of the two materials. We probe the charge and magnetic properties of the system by measuring the dependence of its optical response on an out-of-plane magnetic field and on the gate-tuned carrier density. At half-filling of the first hole moire superlattice band, we observe a Mott insulating state with antiferromagnetic Curie-Weiss behaviour, as expected for a Hubbard model in the strong-interaction regime2,3,7-9. Above half-filling, our experiment suggests a possible quantum phase transition from an antiferromagnetic to a weak ferromagnetic state at filling factors near 0.6. Our results establish a new solid-state platform based on moire superlattices that can be used to simulate problems in strong-correlation physics that are described by triangular-lattice Hubbard models.

568 citations

Posted Content
TL;DR: In this paper, a new diagrammatic technique is developed to describe pseudogap formation in the Hubbard-like models, which utilizes an exact transition to the dual set of variables, and therefore becomes possible to treat the irreducible vertices of an effective single-impurity problem as small parameters.
Abstract: A new diagrammatic technique is developed to describe nonlocal effects (e.g., pseudogap formation) in the Hubbard-like models. In contrast to cluster approaches, this method utilizes an exact transition to the dual set of variables, and it therefore becomes possible to treat the irreducible vertices of an effective {\it single-impurity} problem as small parameters. This provides a very efficient interpolation between weak-coupling (band) and atomic limits. The antiferromagnetic pseudogap formation in the Hubbard model is correctly reproduced by just the lowest-order diagrams.

161 citations

Journal ArticleDOI
TL;DR: In this article, the correlated electronic structure of infinite-layer compounds with finite hole doping was compared from an advanced first-principles many-body perspective, showing that the self-doped nickelate remains non-insulating even for large interaction strength.
Abstract: The correlated electronic structure of the infinite-layer compounds ${\mathrm{NdNiO}}_{2}$ and ${\mathrm{SrCuO}}_{2}$ at stoichiometry and with finite hole doping is compared. Key differences are elucidated from an advanced first-principles many-body perspective. Contrary to the charge-transfer insulating cuprate, the self-doped nickelate remains noninsulating even for large interaction strength, though the Ni-${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ spectral weight is also gapped in that limit. Hybridization between $\mathrm{Ni}(3d)$ and $\mathrm{Nd}(5d)$ is crucial for the appearance of the self-doping band. Upon realistic hole doping, ${\mathrm{Sr}}_{1\ensuremath{-}y}{\mathrm{CuO}}_{2}$ shows the expected mixed oxygen-Cu-${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ (Zhang-Rice) states at low energy. In the case of ${\mathrm{Nd}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{NiO}}_{2}$, the self-doping band is shifted to higher energies and a doping-dependent ${d}_{{z}^{2}}$-versus-${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ competition on Ni is revealed. The absence of prominent Zhang-Rice physics in infinite-layer nickelates might be relevant to understand the notable difference in the superconducting ${T}_{\mathrm{c}}$'s.

152 citations

Journal ArticleDOI
TL;DR: In this paper, a comparative study of state-of-the-art quantum many-body methods is performed using the half-filled Hubbard model at weak coupling as testing grounds, with two numerically exact methods (diagrammatic and determinantal quantum Monte Carlo) serving as a benchmark.
Abstract: The Hubbard model represents the fundamental model for interacting quantum systems and electronic correlations. Using the two-dimensional half-filled Hubbard model at weak coupling as testing grounds, we perform a comparative study of a comprehensive set of state of the art quantum many-body methods. Upon cooling into its insulating antiferromagnetic ground-state, the model hosts a rich sequence of distinct physical regimes with crossovers between a high-temperature incoherent regime, an intermediate temperature metallic regime and a low-temperature insulating regime with a pseudogap created by antiferromagnetic fluctuations. We assess the ability of each method to properly address these physical regimes and crossovers through the computation of several observables probing both quasiparticle properties and magnetic correlations, with two numerically exact methods (diagrammatic and determinantal quantum Monte Carlo) serving as a benchmark. By combining computational results and analytical insights, we elucidate the nature and role of spin fluctuations in each of these regimes and explain, in particular, how quasiparticles can coexist with increasingly long-range antiferromagnetic correlations in the metallic regime. We also critically discuss whether imaginary time methods are able to capture the non-Fermi liquid singularities of this fully nested system.

123 citations

References
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Journal ArticleDOI
TL;DR: In this paper, Ba−La−Cu−O system, with the composition BaxLa5−xCu5O5(3−y) have been prepared in polycrystalline form, and samples with x=1 and 0.75,y>0, annealed below 900°C under reducing conditions, consist of three phases, one of them a perovskite-like mixed-valent copper compound.
Abstract: Metallic, oxygen-deficient compounds in the Ba−La−Cu−O system, with the composition BaxLa5−xCu5O5(3−y) have been prepared in polycrystalline form. Samples withx=1 and 0.75,y>0, annealed below 900°C under reducing conditions, consist of three phases, one of them a perovskite-like mixed-valent copper compound. Upon cooling, the samples show a linear decrease in resistivity, then an approximately logarithmic increase, interpreted as a beginning of localization. Finally an abrupt decrease by up to three orders of magnitude occurs, reminiscent of the onset of percolative superconductivity. The highest onset temperature is observed in the 30 K range. It is markedly reduced by high current densities. Thus, it results partially from the percolative nature, bute possibly also from 2D superconducting fluctuations of double perovskite layers of one of the phases present.

10,272 citations


"Diagrammatic routes to nonlocal cor..." refers background in this paper

  • ...Non-local correlations, on the other hand, are at the heart of some of the most fascinating physical phenomena such as high-temperature superconductivity (Bednorz and Müller, 1986) and quantum criticality (v. Löhneysen et al., 2007)....

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Journal ArticleDOI
Philip W. Anderson1
TL;DR: In this article, a simple model for spin diffusion or conduction in the "impurity band" is presented, which involves transport in a lattice which is in some sense random, and in them diffusion is expected to take place via quantum jumps between localized sites.
Abstract: This paper presents a simple model for such processes as spin diffusion or conduction in the "impurity band." These processes involve transport in a lattice which is in some sense random, and in them diffusion is expected to take place via quantum jumps between localized sites. In this simple model the essential randomness is introduced by requiring the energy to vary randomly from site to site. It is shown that at low enough densities no diffusion at all can take place, and the criteria for transport to occur are given.

9,647 citations

Journal ArticleDOI
TL;DR: In this article, a review of recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases is presented, focusing on effects beyond standard weakcoupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation.
Abstract: This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

6,601 citations

Journal ArticleDOI
TL;DR: A review of the metal-insulator transition can be found in this article, where a pedagogical introduction to the subject is given, as well as a comparison between experimental results and theoretical achievements.
Abstract: Metal-insulator transitions are accompanied by huge resistivity changes, even over tens of orders of magnitude, and are widely observed in condensed-matter systems. This article presents the observations and current understanding of the metal-insulator transition with a pedagogical introduction to the subject. Especially important are the transitions driven by correlation effects associated with the electron-electron interaction. The insulating phase caused by the correlation effects is categorized as the Mott Insulator. Near the transition point the metallic state shows fluctuations and orderings in the spin, charge, and orbital degrees of freedom. The properties of these metals are frequently quite different from those of ordinary metals, as measured by transport, optical, and magnetic probes. The review first describes theoretical approaches to the unusual metallic states and to the metal-insulator transition. The Fermi-liquid theory treats the correlations that can be adiabatically connected with the noninteracting picture. Strong-coupling models that do not require Fermi-liquid behavior have also been developed. Much work has also been done on the scaling theory of the transition. A central issue for this review is the evaluation of these approaches in simple theoretical systems such as the Hubbard model and $t\ensuremath{-}J$ models. Another key issue is strong competition among various orderings as in the interplay of spin and orbital fluctuations. Experimentally, the unusual properties of the metallic state near the insulating transition have been most extensively studied in $d$-electron systems. In particular, there is revived interest in transition-metal oxides, motivated by the epoch-making findings of high-temperature superconductivity in cuprates and colossal magnetoresistance in manganites. The article reviews the rich phenomena of anomalous metallicity, taking as examples Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Ru compounds. The diverse phenomena include strong spin and orbital fluctuations, mass renormalization effects, incoherence of charge dynamics, and phase transitions under control of key parameters such as band filling, bandwidth, and dimensionality. These parameters are experimentally varied by doping, pressure, chemical composition, and magnetic fields. Much of the observed behavior can be described by the current theory. Open questions and future problems are also extracted from comparison between experimental results and theoretical achievements.

5,781 citations

Journal ArticleDOI
TL;DR: The dynamical mean field theory of strongly correlated electron systems is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition.
Abstract: We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.

5,230 citations


"Diagrammatic routes to nonlocal cor..." refers background or methods in this paper

  • ...In ED, the two-particle Green’s function (1) can be computed with a relatively simple algorithmic extension of the standard ED implementation used in the context of DMFT (Georges et al., 1996)....

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  • ...The Lanczos algorithm (Georges et al., 1996), which simplifies the calculation of the single-particle Green’s function, cannot directly be applied to the two-particle Green’s function....

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  • ...They bring forth, among others, quasiparticle renormalizations, Mott-Hubbard metal-insulator transitions, orbital, charge and magnetic ordering, see Georges et al., 1996 for a review....

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  • ...For more details of the method and its multiorbital extensions, see the reviews of Georges et al., 1996 and Held, 2007, and for a first reading Kotliar and Vollhardt, 2004....

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