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

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

Density-matrix formalism with three-body ground-state correlations

A density-matrix formalism which includes the effects of three-body ground- state correlations is applied to the standard Lipkin model. The reason to consider the complicated three-body correlations is that the truncation scheme of reduced density matrices up to the two-body level does not give satisfactory results to the standard Lipkin model. It is shown that inclusion of the three-body correlations drastically improves the properties of the ground states and excited states. It is pointed out that lack of mean-field effects in the standard Lipkin model enhances the relative importance of the three-body ground-state correlations. Formal aspects of the density-matrix formalism such as a relation to the variational principle and the stability condition of the ground state are also discussed. It is pointed out that the three-body ground-state correlations are necessary to satisfy the stability condition

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

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

Quadrupole resonances in unstable oxygen isotopes in time-dependent density-matrix formalism

The strength functions of quadrupole modes in the unstable oxygen isotopes 22O and 24O are calculated using an extended version of the time-dependent Hartree-Fock theory known as the time-dependent density-matrix theory (TDDM). It is found that TDDM gives the lowest quadrupole states which are energetically shifted upward and become significantly collective due to the coupling to two-body configurations. It is pointed out that these features of the lowest quadrupole states are similar to those obtained in the quasi-particle random phase approximation.Comment: 6 pages, 6 figure

Effect of nonmagnetic impurities on stripes in high-Tc cuprates

We perform the numerically exact diagonalization study of the t-J model with nonmagnetic impurities to clarify the relation between Zn impurities and the stripes. By examining the hole-hole correlation function for a two-hole \sqrt{18}x\sqrt{18} cluster with a single impurity, we find that the impurity has a tendency to stabilize vertical charge stripes. This tendency is caused by the gain of the kinetic energy of holes moving along the stripes that are formed avoiding the impurity.Comment: 3 pages including 2 figures. Proceedings for ISS2000 (Tokyo, October 2000). To be published in Physica