Quantum Phase State Of One-dimensional Anisotropic Extended Hubbard Model

One-dimensional electronic systems have been extensively studied,not only driven by theoretical interest,but also by the study of traditional one-dimensional materials.In this dimension,the phase space of the particle scattering makes the electron correlation highly correlated,so the interacting one-dimensional system exhibits anomalous features that cannot be captured by the general Fermi liquid theory.Over the years,research has been devoted to the effects of various interactions on the ground state phase diagram.In particular,recent experimental advances in cold fermion gas of atoms and molecules have stimulated the study of one-dimensional lattice systems beyond the conventional Hubbard approximation.To be sure,the Hubbard model is important in multibody systems research.The Hubbard model was originally used to describe the problem of strong electron correlation in narrow-band insulators,which was subsequently used to study a large number of phenomena observed in experiments.Although it is simple,it does show that any small in-place rejection has a significant effect on the electrodynamics,causing the one-dimensional electronic system to enter Mott insulator,which is characterized by a half full spin density wave phase.It is widely believed that the Hubbard model can describe many of the characteristics of a strongly associated electronic system.However,its applicability to real materials is quite limited,so it has been extended to describe the interacting electrons using a large number of extensions to the physically related one-dimensional Hubbard model.This thesis proposes two extended Hubbard models and only discusses the case of weak coupling.The reason for this is also to be able to effectively combine it with field theory.In the first part,we study the ground-state phase diagram of a one-dimensional t-U-J model,at half-filling.In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy,a phase with gapless charge and massive spin excitations,characterized by the coexistence of triplet superconducting and spin density wave instabilities is realized in the ground state.With reduction of the bandwidth,a transition into an insulating phase showing properties of the spin-1/2 XY model takes place.In the case of weakly anisotropic antiferromagnetic exchange the system shows a long-range dimerized(Peierls)ordering in the ground state.The complete weak-coupling phase diagram of the model,including effects of the on-site Hubbard interaction,is obtained.In the second part,we mainly study the spin energy gap phase in the frustrated Hubbard model with transverse spin anisotropy.By using the same method,the phase diagram of the model after considering the frustration interaction is obtained.It is precisely because of the existence of this frustration interaction that the occurrence of the spin energy gap phase is explained.The results of this paper successfully demonstrate the quantum phase of the onedimensional anisotropic extended Hubbard model.