Effects of the Next-Nearest-Neighbor Hopping on the Low-Dimensional Hubbard Model: Ferromagnetism, Antiferromagnetism, and Superconductivity

TL;DR

This paper reviews how adding next-nearest-neighbor hoppings to the Hubbard model enriches its phase diagram, revealing complex magnetic and superconducting phenomena in one- and two-dimensional systems.

Contribution

It provides a comprehensive review of recent computational studies on the phases of the extended Hubbard model with NNN hoppings in low dimensions.

Findings

NNN hoppings induce diverse magnetic and superconducting phases.

Controversies exist regarding the emergence of superconductivity.

Technical challenges hinder definitive conclusions on phase boundaries.

Abstract

The Hubbard model has attracted considerable interest due to its prototypical role in describing strongly interacting electronic systems, such as high-critical-temperature superconductors as well as many novel quantum materials. By introducing next-nearest-neighbor (NNN) hoppings to the Hubbard model, the phase diagram becomes richer, and fascinating phenomena arise in both, one-dimensional chains and square lattices, such as: antiferromagnetism (AFM), ferromagnetism (FM), superconductivity (SC), as well as charge orders, among others. Moreover, NNN hoppings play a fundamental role in understanding effects of doping on magnetism and pairing orders in strongly interacting regimes. In this article, we review the recent progress in understanding the different competing phases of this model in one and two dimensions from a computational perspective. We comment on the pressing technical challenges, illustrate the controversial results concerning the emergence of the SC phase, and conclude with our perspectives on future explorations.