Strong parameter renormalization from optimum lattice model orbitals

Abstract

We revisit the old problem of which is the best single particle basis to express a Hubbard-like lattice model. A rigorous variational solution of this problem leads to equations in which the answer depends in a self-consistent manner on the solution of the lattice model itself. Contrary to naive expectations, for arbitrary small interactions, the optimized orbitals differ from the non-interacting ones, leading also to substantial changes in the model parameters as shown analytically and in an explicit numerical solution for a simple double-well one-dimensional case. At strong coupling, we obtain the direct exchange interaction with a very large renormalization with important consequences for the explanation of ferromagnetism with model hamiltonians. Moreover, in the case of two atoms and two fermions we show that the optimization equations are closely related to reduced density matrix functional theory thus establishing an unsuspected correspondence between continuum and lattice approaches.

11 pages, 2 figures

References in corpus (8)

• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Two Fermions in a double well: Exploring a fundamental building block of the Hubbard model
• Reduced Density Matrix Functional for Many-Electron Systems
• Gutzwiller density functional theory for correlated electron systems
• Phase Diagram of Na${}_x$CoO${}_2$ Studied by Gutzwiller Density Functional Theory
• Gutzwiller Density Functional Theory: a formal derivation and application to ferromagnetic nickel
• Mean photon number dependent variational method to the Rabi model
• Extended Hubbard model with renormalized Wannier wave functions in the correlated state: beyond the parametrized models