Metal to Insulator Transition in the 2-D Hubbard Model: A Slave Boson Approach

TL;DR

This paper investigates the metal-insulator transition in the 2D Hubbard model using the Kotliar-Ruckenstein slave boson method, identifying critical interaction strengths and phase diagrams on honeycomb and square lattices.

Contribution

It applies the slave boson approach to analyze the metal-insulator transition and phase diagram of the 2D Hubbard model, providing quantitative critical values and magnetic susceptibility behavior.

Findings

Critical U/t for transition is 3.1 on honeycomb lattice.

Gap opens with (U-U_c) behavior near transition.

Magnetic susceptibility peaks in strong coupling regime.

Abstract

We use the Kotliar-Ruckenstein slave boson technique to treat the strong correlation of the Hubbard model. In a first part we discuss the metal to insulator transition that is occurring on the honeycomb lattice at half filling. We find the critical value for the interaction strength to be U/t=3.1. Above it a gap opens in the spectrum which behaves like (U-U_c) in the vicinity of the transition, and like U for strong coupling. In a second part we calculate the phase diagram of the Hubbard model on the square lattice at finite temperature. The Mermin-Wagner theorem is fulfilled in the largest part of the phase diagram. In the strong coupling regime, the uniform magnetic susceptibility shows a maximum in its doping dependence in agreement with numerical simulations.