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.

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

Recently, films created by incorporating metallic nanoparticles into organic or polymeric materials have demonstrated electrical bistability, as well as the memory effect, when subjected to an electrical bias. Organic and polymeric digital memory devices based on this bistable electronic behavior have emerged as a viable technology in the field of organic electronics. These devices exhibit fast response speeds and can form multiple-layer stacking structures, demonstrating that organic memory devices possess a high potential to become flexible, ultrafast, and ultrahigh-density memory devices. This behavior is believed to be related to charge storage in the organic or polymer film, where devices are able to exhibit two different states of conductivity often separated by several orders of magnitude. By defining the two states as “1” and “0”, it is now possible to create digital memory devices with this technology. This article reviews electrically bistable devices developed in our laboratory. Our research has stimulated strong interest in this area worldwide. The research by other laboratories is reviewed as well.

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Electrical Switching and Bistability in Organic/Polymeric Thin Films and Memory Devices

In an electric field, the flow of electrons in a solid produces an entropy current in addition to the familiar charge current. This is the Peltier effect, and it underlies all thermoelectric refrigerators. The increased interest in thermoelectric cooling applications has led to a search for more efficient Peltier materials and to renewed theoretical investigation into how electron-electron interaction may enhance the thermopower of materials such as the transition-metal oxides. An important factor in this enhancement is the electronic spin entropy, which is predicted to dominate the entropy current. However, the crucial evidence for the spin-entropy term, namely its complete suppression in a longitudinal magnetic field, has not been reported until now. Here we report evidence for such suppression in the layered oxide Na(x)Co2O4, from thermopower and magnetization measurements in both longitudinal and transverse magnetic fields. The strong dependence of thermopower on magnetic field provides a rare, unambiguous example of how strong electron-electron interaction effects can qualitatively alter electronic behaviour in a solid. We discuss the implications of our finding--that spin-entropy dominates the enhancement of thermopower in transition-metal oxides--for the search for better Peltier materials.

https://arxiv.org/pdf/cond-mat/0406125.pdf

Spin entropy as the likely source of enhanced thermopower in Na x Co 2 O 4

The present situation in theoretical and experimental studies on one-dimensional magnetic systems is fully discussed. Equal-time as well as the dynamic properties are included with an emphasis on the latter. Four model systems are examined in detail: TMMC (Heisenberg antiferromagnet), CsNiF3 (planar ferromagnet), CoCl2. 2NC5H5 (Ising ferromagnet), CuCl2. 2NC5H5 (Heisenberg antiferromagnet with S = ½). The equal-time properties are quite well understood in theory and in experiment but the dynamical properties much less so. The open questions and possible investigations for the future are discussed.

Theoretical and experimental studies on one-dimensional magnetic systems

The ground-state energy E and momentum distribution nk of the electrons are expanded from the atomic limit for the half-filled Hubbard model. The coefficients of expansion are represented by the spin correlation functions of the spin 1/2 Heisenberg model. Using the spin-wave theory, approximate values of coefficients are calculated for the square lattice and the simple cubic lattice. In one dimension, the theory shows a good agreement with the exact solution. An effective spin Hamiltonian for the half-filled Hubbard model with arbitrary hopping integrals is obtained up to the fifth order. It is shown that the fourth term contains four spin interactions.

https://iopscience.iop.org/article/10.1088/0022-3719/10/8/031/pdf

Half-filled Hubbard model at low temperature

We study the thermoelectric power of a narrow-band Hubbard chain with an arbitrary number of electrons per site. The calculations are carried out to the lowest order in the transfer integral. We find a characteristic electron density ($\ensuremath{\rho}=\frac{2}{3}$) below which the thermoelectric power is negative at all temperatures. In contrast, for $\ensuremath{\rho}g\frac{2}{3}$, the thermoelectric power is small and negative only above a characteristic temperature, below which there is a change of sign and slope. We comment on the applicability of these results to the charge-transfer salts of tetracyanoquinodimethan (TCNQ).

Thermoelectric power of the narrow-band Hubbard chain at arbitrary electron density: Atomic limit

Thermoelectric power in Hubbard-model systems with different densities: N-methylphenazinium-tetracyanoquinodimethane (NMP-TCNQ), and quinolinium ditetracyanoquinodimethane

An exact expression is obtained for the partition function of the arbitrary-electron-density Hubbard chain in the infinite-coupling ($U\ensuremath{\rightarrow}\ensuremath{\infty}$) limit. It is shown that the magnetic susceptibility obeys a Curie law, while the orbital contribution to the specific heat corresponds to that of a noninteracting band of spinless fermions. The electronic mobilities in this limit are shown to be infinite.

Strong-Coupling Hubbard Chain

We consider the Hubbard model for electron correlations in solids in the narrow-band regime where the intra-atomic Coulomb repulsion is large compared to the bandwidth. A high-temperature pertubation expansion in the bandwidth is performed to lowest order for the grand partition function. This procedure is carried out both for one-dimensional systems, of interest for the tetracyanoquinodimethan (TCNQ) charge-transfer salts, and for a three-dimensional cubic lattice. Both the specific heat and magnetic susceptibility are computed as functions of temperature and electron density.

High-Temperature Thermodynamics of the Strongly Correlated Hubbard Model at Arbitrary Electron Density

: The authors consider a narrow one dimensional tight binding chain with intra-atomic Coulomb repulsions described in the Hubbard model. The electrons at each site are furthermore assumed coupled to a high frequency local oscillator. In the limit, where the oscillator frequency is large compared to the bandwidth and in the extreme band narrowing regime, for various electron densities, the authors found that: half-filled band ground state is an antiferromagnetic insulator; one-third filled band is a diamagnetic insulator; one-quarter filled band is a weakly coupled system of bound singlet pairs somewhat reminiscent of superconductivity. (Modified author abstract)

G. Beni

Papers

Thermoelectric power of the narrow-band Hubbard chain at arbitrary electron density: Atomic limit

Thermoelectric power in Hubbard-model systems with different densities: N-methylphenazinium-tetracyanoquinodimethane (NMP-TCNQ), and quinolinium ditetracyanoquinodimethane

Strong-Coupling Hubbard Chain

High-Temperature Thermodynamics of the Strongly Correlated Hubbard Model at Arbitrary Electron Density

Low-temperature properties of the one-dimensional polaron band. I. Extreme-band-narrowing regime