Numerical Study of Hubbard Model for Iron-based Superconductors

This thesis addresses the numerical and analytical study of the iron-based superconductors, mainly using the multi-orbital Hubbard model and Hartree-Fock approximation. The text starts with an introduction to the new iron-based superconductors, followed by a theoretical description of the multi-orbital Hubbard model and Hartree-Fock approximations. The numerical study of the Hubbard model in momentum space is described next, where the phase diagrams for three- and five-orbital Hubbard models are provided. The physically ``realistic" regime of couplings is highlighted, to guide future theoretical work into the proper region of parameters of Hubbard models for iron-based superconductors. What goes next is the numerical investigation of the two-orbital Hubbard model for the pnictides, using the real-space Hartree-Fock approximation on finite clusters. In this study, the charge stripes states are stabilized, upon electron doping. The observed patterns correspond to charge stripes oriented perpendicular to the direction of the spin stripes of the undoped magnetic ground state. After the iron pnictides, the numerical study of the magnetic state of K_0.8Fe_1.6Se₂[potassium iron selenide] is presented, by applying the real-space Hartree-Fock approximation to the five-orbital Hubbard model. This study employed a 10×10 iron cluster with iron vacancies order. An insulating state with the same spin pattern as observed experimentally, involving 2×2 ferromagnetic plaquettes coupled with one another antiferromagnetically, is found to be stable in the phase diagram of the Hubbard model at intermediate Hubbard and Hund couplings. Another similar study of the magnetic state of the two-leg ladder selenide compound BaFe₂Se₃[barium iron selenide] has unveiled a dominant spin arrangement involving ferromagnetically ordered 2×2 iron-superblocks, that are antiferromagnetically coupled among them, and also another state with parallel spins along the rungs and antiparallel along the legs of the ladders. Both of these two states are observed via neutron scattering experiments. Finally, the magnetic phase diagram of a five-orbital Hubbard model for the iron-based superconductors is studied varying the electronic density n and the Hubbard interaction U, at a fixed Hund coupling J/U=0.25. Several qualitative trends and a variety of competing magnetic states are observed in this investigation.