Mean field approaches (e.g., Hartree-Fock or density functional theory) have been successful in describing various materials, but fail when the electrons in the system become strongly correlated. Strong correlation typically occurs when electrons become localized, density fluctuations vary widely over the system, and bands crossing the Fermi energy have a narrow bandwidth. This is the case, for instance, in transition metal-compounds, rare-earth compounds, and organic conductors. To improve the description of the correlated electrons, we use many-body perturbation techniques, such as the GW approximation and the random phase approximation. However, these techniques do not suffice when simulating strongly correlated materials.
Strong correlation leads to unusual electronic and magnetic behaviour, with a wide range of technological applications, such as Mott insulation, high-temperature superconductivity and Hall resistivity. To simulate these exotic properties we need to apply more advanced techniques such as tensor networks or quantum Monte Carlo. These techniques are limited to relatively small and simple systems due to their computational cost. Therefore, we construct effective Hamiltonians, where higher accuracy calculations are conducted in a lower dimensional space made of the specific electronic bands that are responsible for the strong electron correlations, see the figure below.
This methodology consists of three parts. First, the electronic structure of the material is determined via a mean field technique (e.g., density functional theory) for which the bands that exhibit strong correlation are selected. Second, the effective Hamiltonian for the lower dimensional space is constructed via a localization of the selected bands (e.g., Wannierization) and their evaluation of the renormalized interactions (e.g., determined via the constrained random phase approximation). Third, the effective Hamiltonian is solved with methods that accurately take electron correlation into account (e.g., tensor networks).
This research line is a collaboration with the Quantum Group of professor Frank Verstraete, which has ample expertise in tensor networks, the theory of quantum entanglement, and its application to condensed matter systems.
