Many-body theory

Freed, K. F. [1971] Many-Body Theories of the Electronic Structure of Atoms and Molecules , Annual Review of Physical Chemistry, 22, p. 313. 

Goldstone, J., Proc. Roy. Soc. [London] A239, 267, Derivation of the Brueckner many-body theory. ... 

Lindgren, I. and Morrison, J. (1986) Atomic Many-Body Theory, Springer-Verlag, Berlin. 

Let us recall that the Hohenberg-Kohn theorems allow us to construct a rigorous many-body theory using the electron density as the fundamental quantity. We showed in the previous chapter that in this framework the ground state energy of an atomic or molecular system can be written as... 

It is important to realize that each of the electronic-structure methods discussed above displays certain shortcomings in reproducing the correct band structure of the host crystal and consequently the positions of defect levels. Hartree-Fock methods severely overestimate the semiconductor band gap, sometimes by several electron volts (Estreicher, 1988). In semi-empirical methods, the situation is usually even worse, and the band structure may not be reliably represented (Deak and Snyder, 1987 Besson et al., 1988). Density-functional theory, on the other hand, provides a quite accurate description of the band structure, except for an underestimation of the band gap (by up to 50%). Indeed, density-functional theory predicts conduction bands and hence conduction-band-derived energy levels to be too low. This problem has been studied in great detail, and its origins are well understood (see, e.g., Hybertsen and Louie, 1986). To solve it, however, requires techniques of many-body theory and carrying out a quasi-particle calculation. Such calculational schemes are presently prohibitively complex and too computationally demanding to apply to defect calculations. 

These values of A and U have been obtained by using the Argonne v i two-body force [20] both in the BHF and in the variational many-body theories. However, the required repulsive component ( U) is much weaker in the BHF approach, consistent with the observation that in the variational calculations usually heavier nuclei as well as nuclear matter are underbound. Indeed, less repulsive TBF became available recently [21] in order to address this problem. 

M. Baldo, The many body theory of the nuclear equation of state in Nuclear Methods and the Nuclear Equation of State, 1999, Ed. M. Baldo, World Scientific, Singapore. 

If we understand FM or magnetic properties of quark matter more deeply, we must proceeds to a self-consistent approach, like Hartree-Fock theory, beyond the previous perturbative argument. In ref. [11] we have described how the axial-vector mean field (AV) and the tensor one appear as a consequence of the Fierz transformation within the relativistic mean-field theory for nuclear matter, which is one of the nonperturbative frameworks in many-body theories and corresponds to the Hatree-Fock approximation. We also demonstrated... 

Adoption of a many-body theory that is systematically improvable (at least in principle) and testable for its numerical convergence ... 

The numerical determination of E grr by the use of many-body theory is a formidable task, and estimates of it based on E j and E p serve as important benchmarks for the development of methods for calculating electron correlation effects. The purpose of this work is to obtain improved estimates of Epp by combining the leading-order relativistic and many-body effects which have been omitted in Eq. (1) with experimentally determined values of the total electronic energy, and precise values of Epjp. We then obtain empirical estimates of E grr for the diatomic species N2, CO, BF, and NO using Epip and E p and the definition of E g in Eq. (1). 

For systems containing light elements, however, Eq. (2) currently offers the most accurate method for calculating of Ep from first principles and for the estimation of E g,.,. for the calibration of non-relativistic many-body theory. For diatomic molecules high precision accurate numerical methods are available for the calculation of Epp, and, furthermore, Egg,., is about an order of magnitude larger than Ep for light elements. 

At this point one can apply the standard techniques of many-body theory introduced in the previous subsection to obtain (2.40) with//] and 0 ) being replaced by g7 f and Oo), respectively. Using (2.42) one can rewrite Emt as... 

J. Cioslowski, Connected-moments expansion—a new tool for quantum many-body theory. Phys. Rev. Lett. 58, 83 (1987). 

II. Many-Body Theory in Fock-Space Formulation... 

II. MANY-BODY THEORY IN FOCK-SPACE FORMULATION... 

We have already discussed the relations between the four stationarity conditions. In view of their separability, the two irreducible conditions are the right choice in the spirit of a many-body theory in terms of connected diagrams. 

There is a price to pay for the separability, or equivalently for the presence of only connected diagrams. Somewhat like in traditional many-body theory, one must be ready to accept so-caUed EPV (exclusion-principle violating) cumulants. Typical EPV cumulants are nonvanishing kk for k> n, while yj = 0 for k > n. 

D. J. Thouless, The Quantum Mechanics of Many-Body Systems, Academic Press, New York, 1961 P. Nozieres, Le probleme a N corps, Dunod, Paris, 1963 and The Theory of Interacting Fermi Systems, Benjamin, New York, 1964 1. Lindgren and J. Morrison, Atomic Many-Body Theory, Springer, BerUn, 1982. 

D. Mukherjee, ia Recent Progress in Many-Body Theories, Vol. 4, (E. Schachinger, ed.), Plenum, New York, 1995. 

We have chosen here to hint at the density matrix concept, typical of many-body theories, in order to stress that E c is still a two-electrons operator. (For the many body derivation of (20), see ). 

A. Landan, E. Ehav, and U. Kaldor, Intermediate Hamiltonian Fock-Space Coupled-Cluster Method and Applications. In R. F. Bishop, T. Brandes, K. A. Gernoth, N. R. Walet, and Y. Xian (Eds.) Recent Progress in Many-Body Theories, Advances in Quantum Many-Body Theories, Vol. 6. (World Scientific, Singapore, 2002), pp. 355-364 and references therein. 

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