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We present a detailed analysis of the nature of electronic eigenfunctions in one-dimensional quasiperiodic chains based on a clustering idea recently introduced by us [Sil et al., Phys. Rev. B 48, 4192 (1993)], within the framework of the real-space renormalization-group approach. It is shown that even in the absence of translational invariance, extended states arise in a class of such lattices if they possess a certain local correlation among the constituent atoms. We have applied these ideas to the quasiperiodic period-doubling chain, whose spectrum is found to exhibit a rich variety of behavior, including a crossover from critical to an extended regime, as a function of the Hamiltonian parameters. Contrary to prevailing ideas, the period-doubling lattice is shown to support an infinity of extended states, even though the polynomial invariant associated with the trace map is nonvanishing. Results are presented for different parameter regimes, yielding both periodic as well as nonperiodic eigenfunctions. We have also extended the present theory to a multiband model arising from a quasiperiodically arranged array of \ensuremath{\delta}-function potentials on the atomic sites. Finally, we present a multifractal analysis of these wave functions following the method of Godreche and Luck [J. Phys. A 23, 3769 (1990)] to confirm their extended character.

A new type of correlated disorder is shown to be responsible for the appearance of extended electronic states in one-dimensional aperiodic systems like the Thue-Morse lattice. Our analysis leads to an understanding of the underlying reason for the extended states in this system, for which only numerical evidence is available in the literature so far. The present work also sheds light on the restrictive conditions under which the extended states are supported by this lattice., Comment: 11 pages, LaTeX V2.09, 1 figure (available on request), to appear in Physical Review Letters

We discuss a very simple model of a 1-d disordered lattice, in which {\em all} the electronic eigenstates are extended. The nature of these states is examined from several viewpoints, and it is found that the eigenfunctions are not Bloch functions although they extend throughout the chain. Some typical wavefunctions are plotted. This problem originated in our earlier study of extended states in the quasiperiodic copper-mean lattice [ Sil, Karmakar, Moitra and Chakrabarti, Phys. Rev. B (1993) ]. In the present investigation extended states are found to arise from a different kind of correlation than that of the well-known dimer-type., Comment: 9 pages, 1 figure available on request, LaTex version 2.09, SINP-SSMP93-02

A non-perturbative theory is proposed in this article in which an energy independent effective Hamiltonian is obtained for open-shell systems. We have given a diagrammatic version of theory to facilitate the analysis of the problem. The theory has been applied to a model 4-π electron problem, for calculating the lowestπ-π* singlet and triplet energy levels of transbutadiene. Comparison with full Cl calculation indicates the excellent workability of the theory.

In this note, the authors’ recently developed non-perturbative open-shell theory is adapted for direct calculation o f ionisation potential and excitation energy of m any-electron systems. The H -F ground state is used as the “vacuum ” or “ core” in order to achieve a transparent separation o f the ground state energy. An application to a simple 4 π-electron system is discussed as an illustration o f the workability of the theory.