One-dimensional Correlated Systems Particle Excitation Spectra

In condensed matter physics,strong correlated electronic systems are very important since they show unique and interesting properties.Because of the strong electronelectron interaction and electron-phonon interaction,the properties of strong correlated systems are not determined by the simple sum of the electrons' kinetic energy,instead are determined by the collective behavior of all electrons.Correlation effect of electrons and quantum fluctuation of phonon are very important in the low dimensional systems.In Chapter One,we systemically introduced the particle spectral study of one dimensional correlated systems.The Luttinger liquid theory describes the universal and low-energy phenomenal physical properties of one dimensional quantum systems.It is based on the exactly solved Luttinger model.The ground state of this model can be viewed as a non-interacting Boson gas.It is believed that there are at least three unique and universal properties for Luttinger liquid,such as there are no quasi-particle excitations on the Fermi surface;the correlation functions are all pow-law decay;the spin-charge separation exists.The spin-charge separation can be described as:the low-energy excitations of the system are not the quasi-particle excitations,which is different from the Fermi liquid theory,however,they are collective excitations related to spin(no charge) and charge(no spin).These excitations move at different velocities and eventually separate.The angle-resolved photoemission spectroscopy(ARPES) is a very important experimental tool to study spin-charge separation.On the theoretical side,one could calculate the particle spectral function to explain and compare the results of ARPES directly.There are a lot of theoretical methods which could be used to study the one dimensional correlated systems,such as exact diagonalization,densitymatrix renomalization and Monte Carlo method.In this dissertation,we introduce the method of exact diagonalization plus cluster perturbation theory.The Charterer Two studies the particle spectral function of one dimensional asymmetric Hubbard model.It is observed that there is a crossover,which is from the spincharge separation of Hubbard model to the quasi-particle excitation picture of Falicov-Kimball model.The low-energy excitations,such as spinon,holon,soliton and quasiparticle excitations,can be observed directly in the spectral functions.This prediction hopefully can be verified by the ARPES.In Chapter Three,though the calculation of spectral function of one dimensional Holstein-Hubbard model,we discussed the effect of electron-phonon interaction on the spin-charge separation in one dimension in detail.It always is a difficult problem to calculated the systems which have electron-phonon interaction.This is determined by the nature of Bosons.We developed a method which bases on the exact diagonalization within an optimized phonon method plus the cluster perturbation theory.It had been proved that this method is very powerful in practice.By comparing the spectral functions,it is found that the retardation effect induced by electron-phonon interaction suppresses the spectral properties of spin-charge separation.Comparing our numerical results with the ARPES results,for example the experimental data of quasi-one dimensional material TTF-TTNQ,the effect of electron-phonon effect can be observed directly.At the same time,in a particular parameter regein,some interesting excitations are found.We believe that they are related to the electron-paring.The Chapter Four introduces some examples of studying the quantum phase transition by exact diagonalization method.We studied a spin tetrahedron chain and a Bose-Fermi mixture.Both of them are very practical model in condensed matter physics.It can be found that the exact diagonalization plays a very important role in the study.A review can be found in Chapter Five.