Origin of Strong Dispersion in Hubbard Insulators

TL;DR

This paper investigates the origin of strong dispersion in the spectral function of the Hubbard model, attributing it to long-range correlated hopping rather than spin fluctuations or free hopping, explaining high energy anomalies.

Contribution

It identifies long-range correlated hopping as the key mechanism behind high-energy dispersion in Hubbard insulators, contrasting with previous explanations.

Findings

Dispersion is due to correlated hopping $ o t^2/U$

High energy anomaly explained by hole motion within sublattice

Dispersion sensitivity to next-nearest-neighbor hopping $t'$

Abstract

Using cluster perturbation theory, we explain the origin of the strongly dispersive feature found at high binding energy in the spectral function of the Hubbard model. By comparing the Hubbard and $t\small{-}J\small{-} 3s$ model spectra, we show that this dispersion does not originate from either coupling to spin fluctuations ($\propto\! J$) or the free hopping ($\propto\! t$). Instead, it should be attributed to a long-range, correlated hopping $\propto\! t^2/U$, which allows an effectively free motion of the hole within the same antiferromagnetic sublattice. This origin explains both the formation of the high energy anomaly in the single-particle spectrum and the sensitivity of the high binding energy dispersion to the next-nearest-neighbor hopping $t^\prime$.