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

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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