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Physical Review C

Collective particle hole excitation in a deformed ground state

W. D. Heiss, Richard H. Lemmer

Published Jun 1, 1984• 6 citations
Publisher

Abstract

It is shown that stable collective particle hole excitations are possible in a generalized Hartree-Fock basis which describes a ground state that has less symmetry than the Hamiltonian. It appears that these collective states remain stable also for strong attractive interaction.[NUCLEAR STRUCTURE Nuclear matter density fluctuations, generalized random phase approximation.]

DOI
10.1103/physrevc.29.2368

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It is shown that stable collective particle hole excitations are possible in a generalized Hartree-Fock basis which describes a ground state that has less symmetry than the Hamiltonian. It appears that these collective states remain stable also for strong attractive interaction.[NUCLEAR STRUCTURE Nuclear matter density fluctuations, generalized random phase approximation.]
We compute the collective-mode spectrum of the fractional-statistics gas using the set of single particle-hole pairs of the Hartree-Fock ground state as a variational basis. We find that the particle-hole interaction reduces the energy of this mode to a finite value but does not cause it to disperse linearly to zero at long wavelengths, as would be expected of a superfluid. We attribute this to a flaw in the variational ground state, implicitly rectified by computing the response functions in the random-phase approximation. The formalism introduced in this paper provides the machinery for performing precise versions of such calculations.
A finite many-particle system can have collective states for which the off-diagonal matrix elements of certain one-particle operators are of the same order of magnitude as the diagonal elements. In such cases it is suggested that the random-phase approximation is in need of generalization. Examples are the uniform translational motion of any system and the rotational motion of deformed nuclei. The generalization is suggested after a review and critical analysis of the Hartree-Fock approximation. The model single-particle wave functions of the latter are replaced by wave functions in a space labeled both by the particle variables and by the quantum numbers of the collective motion. These generalized amplitudes are defined field-theoretically, and a self-consistent scheme for their calculation is obtained from the equations of motion. In addition to the self-consistent potential defined in the enlarged space, the energies of the excited states also turn out to be given by a natural self-consistency requirement. The new calculational scheme is first applied to a systematic restudy of the random-phase approximation where the self-consistency requirement on the energies has previously been overlooked. As a first characteristic application we obtain without "pushing" the total mass of a system in uniform translation, and a reinterpretation of the Hartree-Fock average field.
We study the collective excitation spectrum of a d = 3 site-disordered Anderson - Hubbard model at half-filling, via a random-phase approximation (RPA) about broken-symmetry, inhomogeneous unrestricted Hartree - Fock (UHF) ground states. We focus in particular on the density and character of low-frequency collective excitations in the transverse spin channel. In the absence of disorder, these are found to be spin-wave-like for all but very weak interaction strengths, extending down to zero frequency and separated from a Stoner-like band, to which there is a gap. With disorder present, a prominent spin-wave-like band is found to persist over a wide region of the disorder - interaction phase plane in which the mean-field ground state is a disordered antiferromagnet, despite the closure of the UHF single-particle gap. Site resolution of the RPA excitations leads to a microscopic rationalization of the evolution of the spectrum with disorder and interaction strength, and enables the observed localization properties to be interpreted in terms of the fraction of strong local moments and their site-differential distribution.