Theoretical study of anomalous liquid states in low-dimensional fermion systems

在低维几何的费米子系统中，人们认为存在一种称为托莫纳加-卢廷格液体的反常状态。我们对其性质进行了研究，得到了一些新的结果。1)在自旋自由度存在激发间隙的情况下，研究了格林函数、自旋响应函数和电荷响应函数的谱行为。我们找到了不同于常规相关指数的特征相关指数。2)我们发展了准一维模型的微扰计算，并发现了从纯一维行为到二维行为的交叉。3)研究了电荷密度波与自旋密度波共存的机理和温度依赖关系。特别是使用重整化群技术，我们发现存在两种可能的共存状态，并且作为温度的函数发生交叉。4)考虑自旋-电荷分离，对双层一维费米子系统的基态进行了变分研究。有几个有趣的磁态取决于第二层的密度。本文还研究了电荷密度波的受挫熔化现象。5)研究了电荷局域化在一维条纹中的条纹态的可能性，并将系统分解为局域化自旋区和一维电荷液体。6)利用一维玻色子之间存在短程斥力的模型，研究了格林函数，澄清了与费米子系统的区别

In the fermion systems in low-dimensiorial geometries, it is believed that an anomalous state called as Tomonaga-Luttinger liquid is realized. We have studied several issues about its properties and obtained some new results as follows.1) In the case where there is an excitation gap for the spin degrees of freedom, we have studied the behaviors of spectrum of Green's functions, spin response functions and charge response functions. We have found characteristic correlation exponents which are different from the conventional ones.2) We have developed perturbative calculations for the quasi-one-dimensional model and found a crossover from purely one-dimensional behavior to two-dimensional behaviors.3) We have studied the mechanism and temperature dependence of the coexistence of charge density wave and spin density wave. Especially using a renormalization group technique, we found that there are two possible coexistent states and a crossover occurs as a function of temperature.4) Considering the spin-charge separation, we studied variationally the ground states of two-layered one-dimensional fermion systems. There are several interesting magnetic states depending on the density in the second layer. A frustration-induced melting of the charge density wave has been also investigated.5) We have studied the possibilities of stripe states where charges are localized in one-dimensional stripes and the system is decomposed into localized spin region and one-dimensional charge liquid.6) Using a model in which there is a short-range repulsion between one-dimensional bosons, we have studied the Green's function and clarified the difference from the fermion systems