Variational approach for the two-body problem in a multiband extended-Hubbard model

M. Iskin

doi:10.1016/j.physleta.2024.129781

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arXiv · 2404.01117

Variational approach for the two-body problem in a multiband extended-Hubbard model

M. Iskin

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Abstract

Considering a spin-up and a spin-down fermion in a generic tight-binding lattice with a multi-site basis, we investigate the two-body problem using a multiband extended-Hubbard model with finite-ranged hopping and interaction parameters. We derive a linear eigenvalue problem for the entire two-body spectrum, alongside a nonlinear eigenvalue problem for the bound states in the form of a self-consistency equation. Our results, based on an exact variational approach, suggest potential applications across various lattice geometries. As an illustration, we apply them to the linear-chain model and show that the resultant spin singlet and triplet bound states align well with the existing literature.

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M. Iskin. 2024-04-01. Variational approach for the two-body problem in a multiband extended-Hubbard model. https://doi.org/10.1016/j.physleta.2024.129781

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