Backflow correlations in the Hubbard model: an efficient tool for the metal-insulator transition and the large-U limit

TL;DR

This paper demonstrates that incorporating backflow correlations into the variational wave function significantly enhances the modeling of the Hubbard model, effectively capturing the metal-insulator transition and strong-coupling behavior with short-range correlations.

Contribution

It introduces an efficient backflow correlation approach that improves variational wave functions for the Hubbard model, connecting weak and strong coupling regimes.

Findings

Backflow correlations are short-range and induce effective attraction between holons and doublons.

The metal-insulator transition shows a discontinuity in double occupancy and kinetic energy.

Charge gap estimation aligns with particle-hole excitation methods.

Abstract

We show that backflow correlations in the variational wave function for the Hubbard model greatly improve the previous results given by the Slater-Jastrow state, usually considered in this context. We provide evidence that, within this approach, it is possible to have a satisfactory connection with the strong-coupling regime. Moreover, we show that, for the Hubbard model on the lattice, backflow correlations are essentially short range, inducing an effective attraction between empty (holons) and doubly occupied sites (doublons). In presence of frustration, we report the evidence that the metal to Mott-insulator transition is marked by a discontinuity of the double occupancy, together with a similar discontinuity of the kinetic term that does not change the number of holons and doublons, while the other kinetic terms are continuous across the transition. Finally, we show the estimation of the charge gap, obtained by particle-hole excitations {\it \`a la Feynman} over the ground-state wave function.