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Acta Physica Sinica

SELF-CONSISTENT MEAN FIELD IN MANY-BODY CORRELATION DYNAMICS

Shun-Jin Wang, 中国高等科学技术中心(世界实验室)理论物理中心,兰州大学

Published Jan 1, 1988• 0 citations
Publisher

Abstract

The self-consistent mean field in the many-body correlation dynamics is discussed in detail. It is shown that the self-consistent mean field exists in general in many-body correlation dynamics for both stationary and non-stationary cases. The many-body correlations enter the mean field through the two-body correlation c2 and the corresponding collision term I. The role played by I is twofold i.e., dynamical effects and statistical effects on single particle states. The many-body correlations also manifest their effects on the many-body energy and yield an energy expression different from the conventional expression in the HF-Bruc-kner theory.

DOI
10.7498/aps.37.881

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The self-consistent mean field in the many-body correlation dynamics is discussed in detail. It is shown that the self-consistent mean field exists in general in many-body correlation dynamics for both stationary and non-stationary cases. The many-body correlations enter the mean field through the two-body correlation c2 and the corresponding collision term I. The role played by I is twofold i.e., dynamical effects and statistical effects on single particle states. The many-body correlations also manifest their effects on the many-body energy and yield an energy expression different from the conventional expression in the HF-Bruc-kner theory.
Using the generalized method of self-consistent field developed by one of the authors[4], we discuss various correlation phenomena of many-body systems with a unified viewpoint. The general method of treatment is proposed and compared with the method of perturbation. From the approximation with two-body correlation we obtain, as particular applications, the Bruckner theory of nuclear matter and the Bohm-Pines theory of the collective oscillation of electron,gases. Finally the superconductivity and zero-point oscillations in non-ideal gases are discussed by solving, the bound state problem with the present method and the Gell-mann Low procedure. It is concluded that the method is very effective in treating correlation phenomena.
Nonlocal correlations play an essential role in correlated electron systems, especially in the vicinity of phase transitions and crossovers, where two-particle correlation functions display a distinct momentum dependence. In nonequilibrium settings, the effect of nonlocal correlations on dynamical phase transitions, prethermalization phenomena, and trapping in metastable states is not well understood. In this paper, we introduce a dynamical mean field theory (DMFT) extension to the nonequilibrium two-particle self-consistent (TPSC) approach, which allows to perform nonequilibrium simulations capturing short- and long-ranged nonlocal correlations in the weak-, intermediate-, and strong-correlation regimes. The method self-consistently computes local spin and charge vertices, from which a momentum-dependent self-energy is constructed. Replacing the local part of the self-energy by the DMFT result within this self-consistent scheme provides an improved description of local correlation effects. We explain the details of the formalism and the implementation, and demonstrate the versatility of DMFT+TPSC with interaction quenches and dimensional crossovers in the Hubbard model.
The concept of electronic correlations plays an important role in modern condensed matter physics. It refers to interaction effects which cannot be explained within a static mean‐field picture as provided by Hartree‐Fock theory. Electronic correlations can have a very strong influence on the properties of materials. For example, they may turn a metal into an insulator (Mott‐Hubbard metal‐insulator transition). In these lecture notes I (i) introduce basic notions of the physics of correlated electronic systems, (ii) discuss the construction of mean‐field theories by taking the limit of high lattice dimensions, (iii) explain the simplifications of the many‐body perturbation theory in this limit which provide the basis for the formulation of a comprehensive mean‐field theory for correlated fermions, the dynamical mean‐field theory (DMFT), (v) derive the DMFT self‐consistency equations, and (vi) apply the DMFT to investigate electronic correlations in models and materials.
According to the quantum chaos paradigm, the nature of a system's classical dynamics, whether integrable or chaotic, is universally reflected in the fluctuations of its quantum spectrum. However, since many-body spectra in the mean-field limit are composed of independent single-particle energy levels, their spectral fluctuations always display Poissonian behavior and hence cannot be used to distinguish underlying chaotic from integrable single-particle dynamics. We demonstrate that this distinction can, instead, be revealed from the mean many-body level density (at fixed energy) and its variance after averaging over ensembles representing different types of single-particle dynamics. This is in strong contrast to the energy-averaged mean level density (of a given system) that is assumed not to carry such information and is routinely removed to focus on universal signatures. To support our claim we systematically analyze the role of single-particle level correlations, that enter through Poisson and random matrix statistics (of various symmetry classes) into the ensemble-averaged density of states and its variance, contrasting bosonic and fermionic many-body systems. Our analytical study, together with extensive numerical simulations for systems with N≥5 particles consistently reveal significant differences (up to an order of magnitude for fermions and even larger for bosons) in the mean many-body level densities, depending on the nature of the underlying dynamics. Notably, in the fermionic case Poisson-type single-particle level fluctuations precisely cancel contributions from indistinguishability, such that the average many-body spectral density equals the (Thomas-Fermi) volume term. We further highlight the difference between the mean level density and its variance as functions of the total energy E and the excitation energy Q.
A stochastic transport description for the single-particle density matrix is briefly discussed. It is shown that the stochastic description contains, in addition to incoherent binary collisions, a coherent damping mechanism due to coupling between mean-field fluctuations and single-particle motion, and an expression for the coherent collision term is derived. In the limit of small fluctuations around equilibrium, the collective and single-particle self-energies due to the coherent mechanism are deduced.