The influence of long-range hopping on ferromagnetism in the Hubbard model

TL;DR

This paper investigates how long-range hopping affects ferromagnetism in the Hubbard model, revealing that it stabilizes ferromagnetism for certain electron densities but suppresses it at others, with implications for magnetic phase stability.

Contribution

It introduces a study of long-range hopping effects on ferromagnetism in the Hubbard model using extrapolated small-cluster calculations and a general hopping matrix expression.

Findings

Long-range hopping stabilizes ferromagnetism for electron density n > 1.

Long-range hopping suppresses ferromagnetism for n ≤ 1.

Critical magnetic field for ferromagnetic stability is numerically determined.

Abstract

The phase diagram of the Hubbard model in an external magnetic field is examined by extrapolation of small-cluster exact-diagonalization calculations. Using a general expression for the hopping matrix elements ($t_{ij}\sim q^{|i-j|}$) the influence of long-range hopping (band asymmetry) on ferromagnetism in this model is studied. It is found that the long-range hopping (nonzero $q$) stabilizes ferromagnetism in an external magnetic field for $n > 1$. In the opposite limit $n \leq 1$ the fully polarized ferromagnetic state is generally suppressed with increasing $q$. The critical value of magnetic field $h$ below which the ferromagnetic state becomes unstable is calculated numerically.