Strongly Interacting Fermi Systems: A Series Expansion Study

通过对模型哈密顿量的静态和动态性质进行级数展开，研究了强相互作用费米系统的平衡相。这将包括围绕简单的完全可溶哈密顿量的零温度膨胀，以及高温膨胀。研究的热力学函数包括自由能、相关序参量及其磁化率，以及动量分布函数等一些费米液体的特征量。此外，还将计算实验观测到的动态量的频率矩，如自旋-晶格弛豫率、光散射光谱和光电导率。这项工作的结果将为我们提供对几种凝聚态现象的新见解，包括磁性和超导秩序的存在和相互作用，金属绝缘体跃迁，以及强相关系统中低能激发的费米液体描述的有效性。

Equilibrium phases of strongly interacting Fermi systems will be investigated by developing series expansions for static and dynamic properties of model Hamiltonians. These will include zero temperature expansions around simple exactly soluble Hamiltonians, as well as high temperature expansions. The thermodynamic functions studied will include the free energy, the relevant order parameters and their susceptibilities, and some characteristic Fermi liquid quantities such as the momentum distribution function. In addition, the frequency moments of experimentally observable dynamical quantities such as spin-lattice relaxation rates, the light scattering spectra and the optical conductivity will also be calculated. The results of this work should provide us with novel insight into several condensed matter phenomena including the existence and interplay of magnetic and superconducting order, metal insulator transitions, and the validity of the Fermi liquid description for the low energy excitations in strongly correlated systems.