Study on Low-Dimensional Electron Systems by Conformal Field Theory

近年来，低维关联电子系统引起了人们的广泛兴趣。本研究项目的目的是系统地研究一维和二维关联电子系统的低能性质，在三年的时间里，我们对准一维系统的量子涨落、杂质效应、无序效应等进行了系统的研究。具体而言，我们利用共形场论、玻色化、非线性sigma模型、精确解等方法研究了一维量子自旋系统、混合自旋系统、一维Mott绝缘体、梯形系统、介观系统等问题。用精确解分析混合自旋系统2。ID和梯形系统中的安德森和莫特转换3.量子线电导的Umklapp散射4. Tomonaga-Luttinger液体中的移动的杂质5. Mott绝缘体的光电发射光谱6.混合自旋梯的非线性u模型分析7。2D自旋系统的量子相变8. Mott绝缘子故障9.可积系统的Drude权在此基础上进行了系统的研究，并取得了丰硕的成果。然而，对于与实验的定量比较，仍然存在一些有趣的未解决的问题。这些问题将在今后的工作中进一步考虑。

Recently, low-dimensional correlated electron systems have attracted much interest. The aim of this research project is to study the low-energy properties of one- and two-dimensional correlated electron systems systematically.During three years of this project, we have performed systematic study on quantum fluctuations, impurity effects, disorder effects for quasi-one-dimensional systems. In par-ticular, we have focused on the topics of one-dimensional (1D) quantum spin systems, mixed spin systems, 1D Mott insulator, ladder systems, mesoscopic systems by using con-formal field theory, bosonization, non-linear sigma model, exact solution, etc. We here list the main results obtained in the research project :1. Analysis of mixed spin systems by the exact solution2. Anderson and Mott transitions in ID and ladder systems3. Umklapp scattering for the conductance in quantum wires4. Mobile impurity in Tomonaga-Luttinger liquids5. Photoemission spectra for the Mott insulator6. Non-linear u model analysis of mixedspin ladders7. Quantum phase transitions for 2D spin systems8. Breakdown of the Mott insulator9. Drude weight for integrable systemsIn this way, the systematic research has been performed with fruitful results. However, as for the quantitative comparison with experiments, there still remain several interesting unsolved problems. These problems will be further considered in the future work.