Theoretical Study on Spontaneous Symmetry Breaking in Strongly Correlated Electrons

In the early days of condensed matter physics, the single electron approximation was considered to be a very good approach in order to explore the properties of many systems. However, as time goes on, a variety of new systems have been discovered and many of them, such as high temperature superconductors and manganites, show phenomenas that evidently can not be explained by single electron theories. Spontaneous symmetry breaking is a very important and famous concept in physics, from the Higgs mechanism in particle physics to the spin density wave in condensed matter physics. The present text describes the detailed studies that the author has done, in order to explore the role of electron-electron interaction induced spontaneous symmetry breaking in two different systems: the iron-pnictides and perovskite [111] bilayers. For the iron-pnictides, we firstly derived the t − J model from the two- orbital Hubbard model in the strong coupling limit. The result is totally different from the famous single-orbital t−J model. Following this model, our group calculated the phase diagram of the iron-pnictides via the Lanczos method.[1] Secondly, we calculated the optical conductivity of the iron-pnictides using the three-orbital Hubbard model under the mean-field approximation and obtained the anisotropy of the optical conductivity which agrees with experiments well. We explained this phenomenon by an effective shift of the Fermi surface induced by electron-electron interaction. For the perovskite [111] bilayers, we used the two-orbital Hubbard model under the mean-field approximation to explore how will the electron-electron interaction produce a Chern-insulator when a flat band is present, and also how can domain structures be formed by applying doping to a quantum Hall ferromagnet.