Instability of Tomonaga-Luttinger Liquids and Quantum Phase Transitions

最近，一维电子系统和梯形系统的各种新材料相继被发现。人们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、自旋隙的形成、磁性相变等，特别是Tomonaga-Luttinger液体的不稳定性和相关的量子相变。我们已经在量子相变方面得到了一些有趣的结果，它们被列举如下：(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)可移动杂质对一维电子系统的影响(4)交变磁场中的Haldane带隙(5)一维关联电子系统中的核磁共振弛豫速率(6)动态诱导的Kondo效应(7)正交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)受阻梯形系统中的Kondo效应(11)多元Tomonaga-Luttinger液体的动态响应还存在与实验的定量对比，这将在今后的工作中考虑。

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.