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FOPRA Experiment 49: The Metal-Insulator Transition with Iterated Perturbation Theory (IPT) as Solver for Dynamical Mean-Field Theory (DMFT)

Course 0000100049 in SS 2021

General Data

Course Type practical training
Semester Weekly Hours 2 SWS
Organisational Unit TUPHT30
Lecturers Lode Pollet
Dates

Further Information

Courses are together with exams the building blocks for modules. Please keep in mind that information on the contents, learning outcomes and, especially examination conditions are given on the module level only – see section "Assignment to Modules" above.

additional remarks The purpose of this project is to see the metal-insulator transition in the 2D square-lattice Hubbard model at half filling. Dynamical mean-field theory (DMFT) is arguably the simplest approximation able to see this transition and this partly explains its popularity. The idea behind DMFT is to map the full lattice problem to an effective impurity problem. Moreover, instead of seeking an exact solution for the impurity problem, we restrict ourselves to the iterated perturbation theory (IPT) in the formulation of Kajueter-Kotliar, where the impurity self energy Σ_{imp} is calculated to second order in perturbation theory and arbitrary densities can be taken. To simplify the analysis, we will use a Bethe lattice, where convergence is usually easier while the results vary little compared to the square lattice. Finally, we will use an analytic continuation method to get the spectral function for real frequencies.
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