Hubbard Model with Next-Nearest-Neighbor Hopping Reveals Rich Phase Diagram, Enabling Ferromagnetism, Superconductivity, and Charge Orders

The behaviour of electrons in complex materials remains a central challenge in condensed matter physics, with the Hubbard model serving as a crucial framework for understanding strongly interacting electronic systems, including high-temperature superconductors. Luhang Yang from the University of Tennessee, Knoxville, Adrian E. Feiguin from Northeastern University, and Thomas P. Devereaux, alongside Elbio Dagotto from the University of Tennessee, Knoxville, and Oak Ridge National Laboratory, investigate how adding a subtle change to this model, allowing electrons to hop not just to their nearest neighbours, but also to the next-nearest, dramatically alters its properties. Their work reveals a far richer landscape of potential behaviours, encompassing magnetism, including both antiferromagnetic and ferromagnetic arrangements, and even superconductivity, where materials conduct electricity with no resistance. By computationally exploring this modified model in one and two dimensions, the team sheds light on the complex interplay between these competing phases and advances our understanding of how these exotic states of matter emerge in real materials.

Hubbard Model, Next-Nearest Hopping, Multi-orbital Extensions

Scientists investigate the behavior of interacting electrons in materials, particularly those exhibiting high-temperature superconductivity, using the Hubbard model. This research explores extensions to this model, most notably by incorporating “next-nearest-neighbor” hopping, a process describing how electrons move to atoms further along the material’s lattice. Researchers aim to understand how this additional hopping influences the emergence of various electronic phases, including magnetism and superconductivity. This work represents a significant effort to model complex electron behavior and unlock the secrets of high-temperature superconductivity. The research identifies key themes including the importance of strong electron interactions, the construction of effective models to simplify complex materials, and the competition between different electronic orders. Scientists employ computational techniques, such as quantum Monte Carlo and density functional theory, to explore these phenomena, building a deeper understanding of the underlying mechanisms driving these complex behaviors.

Next-Nearest Hopping Drives Quantum Phase Diversity

The Hubbard model continues to yield new insights into the behavior of strongly interacting electronic systems, particularly high-temperature superconductors. Recent work focuses on extending the model by incorporating next-nearest-neighbor (NNN) hopping, a quantum mechanical process where electrons move to sites beyond their immediate neighbors on the lattice. This addition dramatically enriches the model’s behavior, giving rise to a diverse range of quantum phases including antiferromagnetism, ferromagnetism, superconductivity, and charge ordering. Researchers have demonstrated that NNN hopping fundamentally alters the electronic band structure, creating hole pockets and eliminating perfect Fermi surface nesting. These changes, combined with electron interactions, are expected to promote superconductivity or ferromagnetism, though the interplay of quantum fluctuations complicates predictions. To overcome limitations of perturbative approaches, scientists are employing advanced numerical methods to investigate the Hubbard model with NNN hopping in a non-perturbative manner, focusing on one-dimensional chains and two-dimensional square lattices to provide crucial insights into the low-energy physics and quantum fluctuations within these systems.

Next-Nearest Hopping Drives Novel Phases

Recent computational investigations have significantly advanced understanding of the Hubbard model, a fundamental framework for describing strongly interacting electronic systems, by incorporating the effects of next-nearest-neighbor hopping. Researchers employed techniques such as density matrix renormalization group, quantum Monte Carlo, tensor networks, and exact diagonalization to explore how this additional hopping influences the emergence of various phases, including antiferromagnetism, ferromagnetism, superconductivity, and charge ordering, in both one- and two-dimensional lattices. This work represents a significant step forward in understanding complex electron behavior in materials. These studies reveal a complex interplay between the hopping parameter, the strength of electron interactions, and the resulting ground state properties of the system. The inclusion of next-nearest-neighbor hopping enriches the phase diagram of the Hubbard model, leading to a wider range of possible electronic states compared to the simpler model without this feature. Researchers acknowledge limitations inherent in numerical methods and note that further research is needed to resolve discrepancies and fully map out the phase diagram.