Metal-insulator transition and magnetic ordering in Hubbard models near the Nagaoka limit

TL;DR

This paper investigates the metal-insulator transition and magnetic ordering in Hubbard models near the Nagaoka limit, revealing charge gaps, phase transitions, and doped hole behavior using particle-hole mapping.

Contribution

It introduces a simplified analysis near the ferromagnetic limit and extends understanding of phase transitions and doping effects in Hubbard models.

Findings

2D Hubbard model has a charge gap at half-filling for any finite U.

First-order phase transition to paramagnetic metal as S_z decreases.

Doped holes have a bandwidth of order J in the large U limit.

Abstract

We study the metal-insulator transition and magnetic ordering in the Hubbard model using the particle-hole mapping. The analysis simplifies near the ferromagnetic limit. We find that the two dimensional(2D) Hubbard model has a charge excitation gap at half-filling for any finite U in this region on both the bipartite square lattice and the nonbipartite triangular lattice. In some cases, the system goes through a first-order phase transition to become a paramagnetic metal as $S_{z}$ is lowered. We also discuss the extension to the doped case. We find that in the large U limit, a single doped hole has a bandwidth of order of J rather than t at $S_{z}=0$.