We have examined the ground state of the many-fermion system, using perturbation theory, with particular attention to Brueckner's method. A study of the single-particle propagators in the ground state of the system sheds some light on the relation between the single-particle energies used, for example, in the optical model of nuclear reactions, and Brucekner's self-consistent energies. This leads naturally to the use of a renormalization factor to allow for propagation off the energy shell. It is possible to formulate the perturbation theory entirely in terms of graphs with no fermion self-energy parts, and this method is used to examine the approximations used for this problem, and to relate more closely the calculations of the ground-state energy and of other properties of the ground state.We have examined the ground state of the many-fermion system, using perturbation theory, with particular attention to Brueckner's method. A study of the single-particle propagators in the ground state of the system sheds some light on the relation between the single-particle energies used, for example, in the optical model of nuclear reactions, and Brucekner's self-consistent energies. This leads naturally to the use of a renormalization factor to allow for propagation off the energy shell. It is possible to formulate the perturbation theory entirely in terms of graphs with no fermion self-energy parts, and this method is used to examine the approximations used for this problem, and to relate more closely the calculations of the ground-state energy and of other properties of the ground state.

Physical ReviewJun 15, 195915 citations

Density-functional theory for two noninteracting spinless fermions

F. Aryasetiawan, Malcolm J. Stott

A method is presented for relating a ground-state density distribution to the effective single-particle potential which has this density for its ground state for a noninteracting system of particles. The method is useful for systems consisting of a small number of spinless fermions and in the case of two particles a second-order, nonlinear differential equation relates the density and the effective potential. The question of $v$ representability is addressed through examples of densities for one- and three-dimensional systems. It is found that densities of the form ${e}^{\ensuremath{-}ar}$ for two-particle systems are not ground-state $v$ representable. The added flexibility of three dimensions over one allows an effective potential which does not necessarily have the chosen density as its ground state, but as its lowest nondegenerate state.A method is presented for relating a ground-state density distribution to the effective single-particle potential which has this density for its ground state for a noninteracting system of particles. The method is useful for systems consisting of a small number of spinless fermions and in the case of two particles a second-order, nonlinear differential equation relates the density and the effective potential. The question of $v$ representability is addressed through examples of densities for one- and three-dimensional systems. It is found that densities of the form ${e}^{\ensuremath{-}ar}$ for two-particle systems are not ground-state $v$ representable. The added flexibility of three dimensions over one allows an effective potential which does not necessarily have the chosen density as its ground state, but as its lowest nondegenerate state.

Physical review. B, Condensed matterSep 15, 198648 citations

General Theory of Many-Particle Systems

Stephen J. Gustafson, Israel Michael Sigal

UniversitextJan 1, 20200 citations

Theory of Many-Particle Systems. I

Paul C. Martin, Julian Schwinger

World Scientific series in 20th century physicsMay 1, 2000967 citations

THEORETICAL STUDY OF LOW-ENERGY ELEMENTARY EXCITATIONS IN SPIN-PEIERLS SYSTEM

Xu Jing, Chen Hong, Yumei Zhang +2 more

By using bosonization technique and quantum self-consistent theory, we study the low-energy excitations of a spin-Peierls system. The ground state, one-particle excited state, two-particle bound state are calculated, and it is shown, as the frustration increases, the energy of the ground state decreases while the energy gap of the one- and two-particle states increases. By analysing the asymototic behavior of the longitudinal spin correlation function, we obtain that the two-particle bound state has similar spin structures as those of the singlet ground state. Thus, we regard the bound state as a singlet state, which exists between the ground state and the two-particle continuous excited state. Our results are qualitatively in agreement with the experimental phenomena observed by Ain et al. It is shown that the existence of bound state is one of the spin-Peierls system's characteristic features.By using bosonization technique and quantum self-consistent theory, we study the low-energy excitations of a spin-Peierls system. The ground state, one-particle excited state, two-particle bound state are calculated, and it is shown, as the frustration increases, the energy of the ground state decreases while the energy gap of the one- and two-particle states increases. By analysing the asymototic behavior of the longitudinal spin correlation function, we obtain that the two-particle bound state has similar spin structures as those of the singlet ground state. Thus, we regard the bound state as a singlet state, which exists between the ground state and the two-particle continuous excited state. Our results are qualitatively in agreement with the experimental phenomena observed by Ain et al. It is shown that the existence of bound state is one of the spin-Peierls system's characteristic features.

Acta Physica SinicaJan 1, 20002 citations

v

representability is addressed through examples of densities for one- and three-dimensional systems. It is found that densities of the form ${e}^{\ensuremath{-}ar}$ for two-particle systems are not ground-state

v

representable. The added flexibility of three dimensions over one allows an effective potential which does not necessarily have the chosen density as its ground state, but as its lowest nondegenerate state.