通过扩展Hubbard模型研究低维关联电子系统的量子特性

With the discovery and the application of one-dimensional electronic material, the low-dimensional system in condensed matter physics becomes an increasingly fascinating field. In one-dimensional systems quantum fluctuations are so drastic that correlation effects make these systems show some unexpected properties, moreover, the applicability of energy band theory and average field method is strongly restricted. The one-dimensional extended Hubbard model is regarded both as the most effective model describing quantum properties of correlated electron systems and as an important theoretical test bed for studying novel concepts and methods in the one-dimensional physics. By bosonization, perturbative renormalization group, quasi-classical analysis and numerical calculation, this project study the extended Hubbard model with anisotropic exchange, spin-dependent Coulomb interaction and correlated-hopping (two- and three-body) in the case of the half-filled band and dopant, respectively. This project, generalizing the one-dimensional Hubbard model, aims to add versions of the extended Hubbard model and to develop theories of the description of low-dimensional electron system as well as to provide the specific physical picture for explanation of some experiment phenomena. This work helps people further understand quantum properties of the low-dimensional correlated electron systems.

随着一维电子材料的不断发现和运用，凝聚态物理中的低维系统越来越成为一个充满活力的研究领域。在一维电子系统中量子涨落十分显著，电子间的关联效应使得系统呈现超乎寻常的特性，能带理论和平均场理论的适用性受到严重的限制。一维扩展Hubbard模型是描述低维关联电子系统量子特性的一个最有效的模型，同时又是研究一维物理新颖概念和方法的一种重要理论试验平台。本项目通过玻色化、微扰重整化群理论和半经典分析及数值计算等方法，在半满、掺杂的情况下，分别研究自旋交换各向异性、依赖自旋的库仑作用和关联电子跃迁（二体和三体）下的扩展Hubbard模型。这既增加现有扩展Hubbard模型的形式，又发展低维关联电子系统的理论，为解释一些与关联相关的实验现象提供一定的物理图像。在此基础上，使得人们对低维关联电子系统的量子特性有着更进一步的认识。