Correlation energy hierarchy in two dimensional Hubbard model

J. M. P. Carmelo, D. Baeriswyl, X. Zotos

Hugh G. A. Burton

, 023300]. In this contribution, I investigate the accuracy of this tUPS hierarchy for strongly-correlated Hamiltonians. I consider the picket-fence pairing Hamiltonian and the two-dimensional Hubbard lattice, which collectively describe a range of strong correlation mechanisms found in molecules. Numerical results demonstrate that highly accurate energies can be achieved with a compact approximation for both weak and strong correlation in the Hubbard model, and the repulsive pairing regime. These data provide valuable insights into the applicability of the tUPS hierarchy for strong electron correlation.

Stéphane Daul, Michael Dzierzawa

Walter Metzner

The functional renormalization group is an ideal tool for dealing with the diversity of energy scales and competition of correlations in interacting Fermi systems. Starting point is an exact hierarchy of flow equations which yields the gradual evolution from a microscopic model Hamiltonian to the effective action as a function of a continuously decreasing energy cutoff. Suitable truncations of the hierarchy have recently led to powerful new approximation schemes. I review applications of the functional renormalization group to the two-dimensional Hubbard model and to one-dimensional Luttinger liquids with impurities.

Qing-Wei Wang, Yu-Liang Liu

K. A. Chao, Rishabh Kishore, I. C. da Cunha Lima

The authors have investigated the Fedro-Wilson theory (1975) to obtain a hierarchy of differential equations for the correlation functions. An approximation is suggested for the truncation of the hierarchy of equations. The result is applied to the weakly correlated Hubbard model to calculate the quasi-particle energy.