Instability of Tomonaga-Luttinger Liquids and Quantum Phase Transitions

近年来，人们在一维电子体系和梯形体系中发现了许多新材料。观察到了各种惊人的现象。本研究的目的是研究一维和二维关联电子系统的量子涨落、自旋能隙形成、磁相变等，特别强调Tomonaga-Luttinger液体的不稳定性和相关的量子相变。我们得到了一些关于量子相变的有趣结果，这些结果如下：（1）混合自旋系统中的量子相变（2）一维Mott绝缘体的光电子能谱（3）移动的杂质对一维电子系统的影响（4）交变磁场中的Haldrongggap（5）一维关联电子系统中的NMR弛豫率（6）动力学诱导的Kondo效应（7）非对称二聚体系统中的量子相变（8）量子点中的电子关联（9）碳纳米管中的Kondo效应（10）受抑梯形系统中的磁化和空穴掺杂效应（11）多组分Tomonaga-Luttinger液体虽然已经进行了系统的研究，但仍然存在与实验的定量比较，这将在未来的工作中考虑。

Recently, a variety of new materials have been found for one-dimensional electron systems as well as ladder systems. Various striking phenomena have been observed. The aim of this research is to study quantum fluctuations, spin-gap formation, magnetic phase transitions, etc, for one- and two-dimensional correlated electron systems with particular emphasis on the instability of the Tomonaga-Luttinger liquid and related quantum phase transitions. We have obtained a number of interesting results on the quantum phase transitions, which are listed below:(1) Quantum Phase Transitions in Mixed Spin Systems(2) Photoemission Spectra for the 1D Mott insulator(3) Effect of a Mobile Impurity on 1D Electron Systems(4) Haldane Gap in Alternating Magnetic Fields(5) NMR Relaxation Rate in 1D Correlated Electron Systems(6) Dynamically induced Kondo effect(7) Quantum Phase Transitions in Orthogonal-Dimer System(8) Electron Correlations in a Quantum Dot(9) Kondo Effect in Carbon Nanotubes(10) Magnetization and Hole-Doping Effect in a Frustrated Ladder system(11) Dynamical Responses of Multicomponent Tomonaga-Luttinger LiquidsAlthough the research has been performed systematically, there still remains the quantitative comparison with experiments, which will be considered in the future work.