Correlated Ground-State Wavefunctions

Hamed Pakatchi

A prominent class of model FQH ground states is those realized as correlation function of Zk(r)-algebras. In this paper, we study the interplay between these algebras and their corresponding wavefunctions. In the hopes of realizing these wavefunctions as a unique densest zero energy state, we propose a generalization for the projection Hamiltonians. Finally, using techniques from invariants of binary forms, an ansatz for computation of correlations 〈ψ(z1)⋯ψ(z2k)〉∏i<j(zi−zj)2r/k is devised. We provide some evidence that, at least when r=2, our proposed Hamiltonian realizes Zk(2)-wavefunctions as a unique ground state.

Federico Becca, Sandro Sorella

Frank W. Bobrowicz

Birte L. Christensen-Dalsgaard

The ground-state wavefunctions for Li - , Na - and K - are calculated using the hyperspherical method. They are analysed and compared with the ground state as well as the first 1 S resonance in H - to reveal the effect of correlation. In order to perform a quantitative comparison an absolute measure of angular and radial correlation based on statistical methods is used and its relevance to characterise correlation in the ground states is discussed.

Tim Freegarde

Yajiang Hao, Yiwang Liu, Xiangguo Yin

In momentum space, we investigate the correlation properties of the ground state of Tonks–Girardeau gases. With Bose–Fermi mapping method, the exact ground state wavefunction in coordinate space can be obtained based on the wavefunction of spin-polarized Fermions. By Fourier transformation we obtain the ground state wavefunction in momentum space, and therefore the pair correlation and the reduced one-body density matrix (ROBDM) in momentum space, whose diagonal part is the momentum distribution. The ROBDM in momentum space is the Fourier transformation of the ROBDM in coordinate space and the pair correlation in momentum space is the Fourier transformation of the reduced two-body density matrix in coordinate space. The correlations in momentum space display larger values only in small momentum region and vanish in most other regions. The lowest natural orbital and occupation distribution in momentum space are also obtained.