Phases And Phase Transitions In A 2D Interaction Model

Electron correlations and quantum fluctuations play an important role in the physi-cal properties. Studies of the electron correlations induced transition are of considerable interest and importance in condensed matter physics. The ground state may be quite different in essence in a same model when the dimensionality is different. This thesis focus on the phase diagram of the half-filled ionic Hubbard and hole-doped extended t-t' Hubbard model. Even though these models have been widely studied in the one dimensional case, the theoretical phase diagram for the two dimensional case was pro-posed only in these years, with the help of the recently developed numerical methods. There are a lot of debates in the two dimensional system, characteristics of some new phases remaining unclear, since the phase diagram is much complicated compared with one dimension, and the numerical methods have various limitations. The main purpose of this thesis is to provide our opinion based on the powerful method, clarifying some open questions.In this thesis, we present a review of a number of related numerically exact ap-proaches to quantum many-body problems. In particular, we focus on the method, so called variational cluster approach (VCA), based on the exact diagonalization of the Hamiltonian matrix. The VCA includes the short-range correlations exactly within a cluster and treats the long-range correlations exceeding the cluster scale on the mean-field level. The SFT allows us to approximate the physics of an infinite system via exact solution of a small isolated system. The VCA has been applied successfully to many systems, allowing us to study the symmetry-breaking phase in particular. We also sur-vey extensions to the methods to calculate properties such as spectral functions, order parameters, investigating the interplay between different phases.The Mott transition and the transition from band to Mott insulator, which can be realized in the half filled ionic Hubbard model, have attracted considerable interest these years. This model has a very rich phase diagram despite its simplicity. Different methods do not show agreement with others, stimulating intensive interest. We inves-tigate the quantum phase transitions in the half-filled ionic Hubbard model on a two-dimensional square lattice using the variational cluster approach (VCA). We present explicit evidence for the tendency toward a novel intermediate phase in this model. This phase is characterized by bond-located magnetization. For weak Coulomb repul-sion U, the system is a band insulator, and then undergoes a transition to the interme-diate phase at the first phase boundary U?Ucl. As U is increased beyond the second transition point Uc2, there occurs a Mott insulator accompanied with a long-range an-tiferromagnetic (AF) order. The bond-located spin density wave competes with the antiferromagnetism while the charge-density modulation exists all the way due to the staggered potential?.In addition, we also study the two-dimensional extended t-t' Hubbard model, adding nearest neighbor repulsion to the Hubbard model with frustration, using the variational cluster approach. There exists a manifest distinction in the half-filled and hole-doped case. The system is a Mott insulator for half filling whereas a pure su-perconducting and coexisting phase under hole-doped condition. We find the system shows a tendency toward the PI which breaks the tetragonal symmetry of the Fermi sur-face. However, a pure superconducting state with isotropic underlying lattice is more favored for weak nearest neighbor repulsion V. As V is increased beyond the critical value, superconductivity is suppressed and the system undergoes a first order transition to the PI. We find that the local density of states (LDOS) shows interesting behavior in the presence of Fermi surface symmetry breaking. The low-energy feature of LDOS is sharp and the spectral weight remarkably transfers from low-energy peaks to the local minimum near the Fermi level. Meanwhile, the high-energy feature remains almost unchanged. Based on these findings, we can establish a potential relationship between the PI and metamagnetic transition in the bilayer ruthenate Sr3Ru2O7...