Strong parameter renormalization from optimum lattice model orbitals

TL;DR

This paper develops a self-consistent variational method to optimize single-particle orbitals in lattice models, revealing significant changes in parameters and implications for ferromagnetism, bridging continuum and lattice theories.

Contribution

It introduces a rigorous variational approach for optimizing orbitals in Hubbard-like models, showing their dependence on interactions and establishing a link to reduced density matrix functional theory.

Findings

Optimized orbitals differ from non-interacting ones even at small interactions.

Strong coupling leads to large renormalization of exchange interactions.

The optimization equations relate to reduced density matrix functional theory.

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.