Hubbard-I approach to the Mott transition

TL;DR

This paper advances the Hubbard-I method by incorporating symmetry considerations and strong coupling expansion to better describe the Mott transition in correlated electron systems, providing new phase diagrams and comparisons with other approaches.

Contribution

It introduces a combined Hubbard-I and strong coupling expansion approach for systems with conserved double occupancy, improving the description of the Mott transition.

Findings

Successful Hubbard-I calculation of the Mott transition in a constrained Hubbard model.

The phase diagram for arbitrary fillings including the Mott transition at half-filling.

Qualitative differences between Hubbard-I and Gutzwiller Approximation results.

Abstract

We expose the relevance of double occupancy conservation symmetry in application of the Hubbard-I approach to strongly correlated electron systems. We propose the utility of a composite method, viz. the Hubbard-I method in conjunction with strong coupling perturbation expansion, for studying systems violating the afore--mentioned symmetry. We support this novel approach by presenting a first successful Hubbard-I type calculation for the description of the metal-insulator Mott transition in a strongly correlated electron system with conserved double occupancies, which is a constrained Hubbard Hamiltonian equivalent to the Hubbard bond charge Hamiltonian with $X=t$. In particular, we obtain the phase diagram of this system for arbitrary fillings, including details of the Mott transition at half-filling. We also compare the Hubbard-I band--splitting Mott transition description with results obtained using the standard Gutzwiller Approximation (GA), and show that the two approximate approaches lead to qualitatively different results. In contrast to the GA applied to the system studied here, the Hubbard-I approach compares favourably with known exact results for the $d=1$ dimensional chain.