Magnetic and Charge Correlations of the 2-dimensional $t-t'-U$ Hubbard model

TL;DR

This study investigates how next-nearest neighbor hopping $t'$ influences magnetic and charge behaviors in the 2D Hubbard model, revealing that negative $t'$ promotes ferromagnetism while positive $t'$ suppresses magnetic fluctuations and encourages charge stripe order.

Contribution

It introduces a spin-rotation invariant slave boson approach to analyze the effects of $t'$ on magnetic and charge correlations in the Hubbard model, highlighting the role of frustration.

Findings

Negative $t'$ favors itinerant ferromagnetism in hole-doped regimes.

Positive $t'$ suppresses magnetic fluctuations and promotes stripe charge order.

Large positive $t'$ is associated with frustrated charge dynamics and magnetic fluctuation suppression.

Abstract

Using a spin-rotation invariant six-slave boson representation, we study the square lattice Hubbard model with nearest-neighbor hopping $t$ and next-nearest neighbor hopping $t'$. We discuss the influence of $t'$ on the charge and magnetic properties. In the hole-doped domain, we find that a negative $t'$ strongly favors itinerant ferromagnetism over any incommensurate phase, especially in the strong coupling regime. For positive $t'$ magnetic fluctuations are suppressed. A tight connection between frustrated charge dynamics and large magnetic fluctuations is pointed out. A clear tendency towards striped charge ordering is found in the regime of large positive $t'$.