Cluster Dynamical Mean Field Theory For Strongly Correlated Electron Systems

Strongly correlated electron system, as its name suggests, include strong Coulombinteractions between the electrons. So it can`t be treat with the perturbation theory witchbased on the description of single electron energy band. Most of the d and f electronicsystem such as transition metal oxides, heavy fermion systems are strongly correlatedelectron system, which exhibit abundant singular quantum phenomenon. People use a newmethod developed in recent decades and named dynamical mean-field theory to studythese phenomena of strongly correlated electron materials. Dynamical mean-field theoryproject lattice models onto quantum impurity models and this mapping is exact in infinitedimensional. But the single impurity approximation cannot deal with physical quantityinclude short-range correlations. Then, people further developed the dynamical mean fieldframework, namely cluster dynamics mean field method witch include nonlocal shortrange correlation and spatial fluctuation.In this paper we choose exact diagonalization method as a impurity solver combinedwith cluster dynamical mean field theory to study the strongly correlated electron system.Firstly, we solve the half-filled Hubbard model, and research the Mott metal insulatorphase transition, then analysis on different physical quantities to determine the phasetransition point. After that, we use the periodic Anderson model to research on thecompetitive order in the heavy fermion materials, and the problem of the competition andcoexistence between antiferromagnetic and superconducting phase in these mechanisms.During this period we improved algorithm of the program so as to effectively improve thecalculation efficiency, and use the computing cluster to make a high performancecomputing. Finally, we analyze the calculated results, and then compare with someexperimental results and theoretical results.