Mott metal-insulator transition in the Hubbard model

TL;DR

This paper investigates the Mott metal-insulator transition in the Hubbard model, analyzing the ground state properties within and beyond the single-site approximation, and discusses implications for real materials.

Contribution

It provides a detailed analysis of the Hubbard model's ground state, highlighting the limitations of the SSA and the instability of the Fermi liquid beyond SSA.

Findings

Within SSA, the ground state is a Mott insulator at critical point.

Beyond SSA, the Fermi liquid becomes unstable, leading to non-normal states.

Additional effects like electron-phonon interactions are needed to explain real transitions.

Abstract

The ground state of the Hubbard model is studied within the single-site approximation (SSA) and beyond the SSA. Within the SSA, the ground state is a typical Mott insulator at the critical point n=1 and U/W=+infty, with n being the electron density per unit cell, W the bandwidth of electrons, and U the on-site repulsion, and is a normal Fermi liquid except for the critical point. Beyond the SSA, the normal Fermi liquid is unstable against a non-normal Fermi liquid state except for a trivial case of U=0 such as a magnetic or superconducting state in two and higher dimensions. In order to explain actual observed metal-insulator transitions, one or several effects among the electron-phonon interaction, multi-band or multi-orbital effects, and effects of disorder should be considered beyond the Hubbard model.