Aspects of the ground state of the $U=\infty$ Hubbard ladder

TL;DR

This paper investigates the ground state properties of the $U= ablafty$ Hubbard ladder, focusing on ferromagnetism and the metal-insulator transition at quarter-filling, using rigorous results and numerical methods to analyze phase boundaries and charge gaps.

Contribution

It provides rigorous and numerical analysis of the ground state phases of the $U= ablafty$ Hubbard ladder, including the critical inter-chain hopping ratio for charge gap opening.

Findings

Ground state spin transitions at $n=0.5$

Charge gap at quarter-filling is $2t_{ot}$

Critical $t_{ot}/t$ for charge gap less than 0.001

Abstract

We consider two aspects of the ground state of the $U=\infty$ Hubbard ladder: ferromagnetism and the metal-insulator transition at quarter-filling. First, we present rigorous results for the $U=\infty$ Hubbard ladder in the limit of the large inter-chain hopping ($t_{\perp}/t\to\infty$). In this limit, the total spin $S$ of the ground state is shown to be zero for the electron density $n\le 0.5$ and its maximum ($S=S_{max}$) for $n>0.5$. The charge gap at quarter-filling is $2t_{\perp}$. We extend these results to finite $t_{\perp}/t$ by means of the density-matrix renormalization group method. We estimate the phase boundaries with respect to spontaneous magnetization and the charge gap at quarter-filling for finite $t_{\perp}/t$. Applying the extended Aharonov-Bohm method, we give numerical evidence that the critical ratio $t_{\perp}/t$, above which the charge gap opens, is less than 0.001. Ferromagnetism in the t-J ladder is briefly discussed.