From Hubbard model to t-J-U model: a canonical transformation formalism, the metal-insulator transition and mean-field state

TL;DR

This paper derives the t-J-U model from the Hubbard model using a canonical transformation, analyzes the metal-insulator transition, and links the metallic state to gossamer superconductivity.

Contribution

It introduces a canonical transformation approach to connect the Hubbard and t-J-U models and explores the metal-insulator transition and superconducting states.

Findings

The t-J-U model can be derived from the Hubbard model at finite U.

The critical Coulomb interaction for metal-insulator transition is lower than previous estimates.

The metallic state can be equivalent to Laughlin's gossamer superconducting state.

Abstract

We prove that the t-J-U model can be deduced from the Hubbard model at a large but finite U by a canonical transformation. We argue that the system may have a metal-insulator transition at a critical on-site Coulomb interaction whose value, however, is smaller than that in previous calculations in which the kinetic energy has a double counting. In a mean field theory and a special choice of the parameters, we show that the metallic state may be equivalent to the gossamer superconducting state proposed by Laughlin recently.