One-dimensional Correlated Systems, Single-particle Excitation And Kinetic Studies

Quantum phonon fluctuation and electronic correlation play an important role determining the characteristic of π-conjugated polymer. Our emphasis in this thesis is on quasi-one-dimensional π-electron models that include both electron-phonon and electron-electron interactions, on which we investigate the one-electron spectral functions, metal-insulator transition, spin-charge separation and time evolution.In this thesis, we present a review of a number of related numerically exact approaches to quantum many-body problems. In particular, we focus on methods based on the exact diagonalization of the Hamiltonian matrix and on methods extending exact diagonalization using renormalization group ideas, i.e., Wilson's Numerical Renor-malization Group(NRG) and White's Density Matrix Renormalization Group(DMRG). These methods are standard tools for the investigation of a variety of interacting quantum systems, especially low-dimensional quantum lattice models. We also survey extensions to the methods to calculate properties such as dynamical quantities(e.g., spectral functions, time-evolution), and discuss recent progress in calculating the time evolution of quantum systems using the DMRG.Using the cluster perturbation theory, we calculate the one-electron spectral function of the one-dimensional spin-1/2 Holstein model at half filling. The cluster Green' s function is obtained by the Lanczos exact diagonalization method within an optimized phonon approach. It is shown that the method allows reliable calculations using a relatively small size cluster and a few optimal phonon bases for the system from weak to strong electron-phonon coupling. In the strong-coupling limit, the spectral function shows the excitation behavior of a bipolaron state with a large gap at the Fermi surface. However, the obtained spectral function displays a metallic character in the weak-coupling regime, which is in accord with the suggestion that the Peierls gap is suppressed by quantum fluctuation of the phonons.Phonon effects on spin-charge separation in one dimension are investigated through the calculation of one-electron spectral functions in terms of the recently developed cluster perturbation theory together with an optimized phonon approach. It is found that the retardation effect due to the finiteness of phonon frequency suppresses the spin-charge separation and eventually makes it invisible in the spectral function. Asignature of electrons pairing in weak interaction regimes was found to be consistent with the existence of a metallic phase.The level of current understanding of the physics of time-dependent strongly correlated quantum systems is far from complete, principally due to the lack of effective controlled approaches. Recently, there has been progress in the development of approaches for one-dimensional systems. We describe recent developments in the construction of numerical schemes for general (one-dimensional) Hamiltonians: in particular, schemes based on exact diagonalization techniques and on the density matrix renormalization group method. We present preliminary results for an extended Su-Schrieffer-Heeger model with nearest-neighbor-interaction and investigate their accuracy by comparing with exact results.The localized phonon modes can be measured to be the 'fingerprint' of localized excitations in polymers. So, within an extended Su-Schrieffer-Heeger model, we made a lattice vibrational analysis of polyacene. In a singly-charged polyacene, the ground state contains an interchain-coupled polaron of quasi-D_2hi symmetry, around which we found thirteen localized modes in total. Among these localized modes, five (three B_2u and two B_3u) are infrared active, six (four A_g and two B_1g) modes are Raman active, and the other two localized modes are asymmetric, which are both infrared active and Raman active. For the case a charged polaron is coupled with a neutral soliton in a finite polyacene chain, the vibrational modes are also calculated to display the coupling effect between self-trapping excitations on phonons. It is found that the localized phonons are determined mainly by the charged polaron, but the number and frequencies of the localized modes are influenced by the existence of the neutral soliton. .