Ferromagnetism in the Hubbard model with a generalized type of hopping

TL;DR

This paper investigates how long-range hopping in the one-dimensional Hubbard model influences ferromagnetism, showing that certain hopping patterns stabilize ferromagnetic states across various interaction strengths and electron concentrations.

Contribution

It introduces a generalized hopping term with power decay and demonstrates its role in stabilizing ferromagnetism in the Hubbard model, providing numerical phase diagrams.

Findings

Long-range hopping stabilizes ferromagnetism over a wide parameter range.

Critical interaction strength $U_c(q)$ is numerically determined.

Ground-state phase diagrams are presented for key cases.

Abstract

The extrapolation of small-cluster exact-diagonalization calculations is used to examine ferromagnetism in the one-dimensional Hubbard model with a generalized type of hopping. It is found that the long-range hopping with power decaying hopping amplitudes ($t_{ij}\sim q^{|i-j|}$) stabilizes the ferromagnetic state for a wide range of electron interactions $U$ and electron concentrations $n$. The critical value of the interaction strength $U_c(q)$ above which the ferromagnetic state becomes stable is calculated numerically and the ground-state phase diagram of the model (in the $U$-$q$ plane) is presented for physically the most interesting cases.