Extended RPA with ground-state correlations

We propose a time-independent method for finding a correlated ground state of an extended time-dependent Hartree-Fock theory, known as the time-dependent density-matrix theory (TDDM). The correlated ground state is used to formulate the small amplitude limit of TDDM (STDDM) which is a version of extended RPA theories with ground-state correlations. To demonstrate the feasibility of the method, we calculate the ground state of 22O and study the first 2+ state and its two-phonon states using STDDM.Comment: 12 pages, 9 figure

Extended RPA with ground-state correlations in a solvable model

The ground states and excited states of the Lipkin model hamiltonian are calculated using a new theoretical approach which has been derived from an extended time-dependent Hartree-Fock theory known as the time-dependent density-matrix theory (TDDM). TDDM enables us to calculate correlated ground states, and its small amplitude limit (STDDM), which is a version of extended RPA theories based on a correlated ground state, can be used to calculate excited states. It is found that this TDDM plus STDDM approach gives much better results for both the ground states and the excited states than the Hartree-Fock ground state plus RPA approach.Comment: 4 pages, 4 figure

Spurious modes in extended RPA theories

Necessary conditions that the spurious state associated with the translational motion and its double-phonon state have zero excitation energy in extended RPA (ERPA) theories which include both one-body and two-body amplitudes are investigated using the small amplitude limit of the time-dependent density-matrix theory (STDDM). STDDM provides us with a quite general form of ERPA as compared with other similar theories in the sense that all components of one-body and two-body amplitudes are taken into account. Two conditions are found necessary to guarantee the above property of the single and double spurious states: The first is that no truncation in the single-particle space should be made. This condition is necessary for the closure relation to be used and is common for the single and double spurious states. The second depends on the mode. For the single spurious state all components of the one-body amplitudes must be included, and for the double spurious state all components of one-body and two-body amplitudes have to be included. It is also shown that the Kohn theorem and the continuity equations for transition densities and currents hold under the same conditions as the spurious states. ERPA theories formulated using the Hartree-Fock ground state have a non-hermiticity problem. A method for formulating ERPA with hermiticity is also proposed using the time-dependent density-matrix formalism.Comment: 15 page

Double giant dipole resonances in time-dependent density-matrix theory

The strength functions of the DGDRs in 16O and 40Ca are calculated using an extended version of TDHF known as the time-dependent density-matrix theory (TDDM). The calculations are done in a self-consistent manner, in which the same Skyrme force as that used for the mean-field potential is used as the residual interaction to calculate two-body correlations. It is found that the DGDR in 16O has a large width due to the Landau damping, although the centroid energy of the DGDR is close to twice the energy of the GDR calculated in RPA. The DGDR in 40Ca is found more harmonic than that in 16O.Comment: 4 pages, 3 figure

Asymmetry of the electronic states in hole- and electron-doped cuprates: Exact diagonalization study of the t-t'-t''-J model

We systematically examine the asymmetry of the electronic states in the hole- and electron-doped cuprates by using the t-t'-t''-J model. Numerically exact diagonalization method is employed for a 20-site square lattice. We impose twisted boundary conditions (BC) instead of standard periodic BC. For static and dynamical correlation functions, averaging procedure over the twisted BC is used to reduce the finite-size effect. We find that antiferromagnetic spin correlation remains strong in electron doping in contrast to the case of hole doping, being similar to the case of the periodic BC. This leads to a remarkable electron-hole asymmetry in the dynamical spin structure factor and two-magnon Raman scattering. By changing the twist, the single-particle spectral function is obtained for all momenta in the Brillouin zone. Examining the spectral function in detail, we find a gap opening at around the k=(pi,0) region for 10% doping of holes (the carrier concentration x=0.1), leading to a Fermi arc that is consistent with experiments. In electron doping, however, a gap opens at around k=(pi/2,pi/2) and persists up to x=0.2, being correlated with the strength of the antiferromagnetic correlation. We find that the magnitude of the gaps is sensitive to t' and t''. A pseudogap is also seen in the optical conductivity for electron doping, and its magnitude is found to be the same as that in the spectral function. We compare calculated quantities with corresponding experimental data, and discuss similarities and differences between them as well as their implications.Comment: 14 pages, 17 figures, Replaced figures, to be published in Phys. Rev.

Eigenstates of the time-dependent density-matrix theory

An extended time-dependent Hartree-Fock theory, known as the time-dependent density-matrix theory (TDDM), is solved as a time-independent eigenvalue problem for low-lying $2^+$ states in $^{24}$O to understand the foundation of the rather successful time-dependent approach. It is found that the calculated strength distribution of the $2^+$ states has physically reasonable behavior and that the strength function is practically positive definite though the non-hermitian hamiltonian matrix obtained from TDDM does not guarantee it. A relation to an extended RPA theory with hermiticity is also investigated. It is found that the density-matrix formalism is a good approximation to the hermitian extended RPA theory.Comment: 8 pages, 1 figur

Relation between the density-matrix theory and the pairing theory

The time-dependent density-matrix theory (TDDM) gives a correlated ground state as a stationary solution of the time-dependent equations for one-body and two-body density matrices. The small amplitude limit of TDDM (STDDM) is a version of extended RPA theories which include the effects of ground state correlations. It is shown that the solutions of the Hartree-Fock Bogoliubov theory and the quasi-particle RPA satisfy the TDDM and STDDM equations, respectively, when only pairing-type correlations are taken into account in TDDM and STDDM.Comment: 11 page