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Physics Letters A

Phase diagram of the one-dimensional Hubbard model with competing intrabond hopping processes

Xin Sun, Hanqin Ding

Published Sep 11, 2026• 0 citations
Publisher
DOI
10.1016/j.physleta.2026.132174

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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, ferromagnetism, 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.
The ground state of the one-dimensional half-filled Penson-Kolb-Hubbard model (with competing single-particle and pair hoppings in the presence of on-site Coulomb repulsion) has been investigated by a real space renormalization group method. The ground state energy, energy gap, local moment and several correlation functions are studied to obtain the phase diagram. The phase diagram consists of a spin density wave (SDW) state, a superconducting (SC) phase and a quasi-metallic phase dominated by short range SC correlations for positive values of the pair hopping amplitude; when this amplitude is negative, the phase diagram contains a near-metallic commensurate charge density wave and an SC phase of pairs with centre-of-mass momentum q= pi apart from an SDW phase.