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  • Open Access

Two-exciton bound states in the Merrifield exciton model

Ning Wu*, Runtian Li, and Dazhi Xu†

  • Center for Quantum Technology Research, and Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, China

  • *Contact author: wunwyz@gmail.com
  • †Contact author: dzxu@bit.edu.cn
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Phys. Rev. B 114, 225127 – Published 16 October, 2026

DOI: https://doi.org/10.1103/9c6b-gk9f

Abstract

Understanding the formation and dynamics of two-exciton bound states (BSs) is crucial for harnessing multiexciton phenomena and designing next-generation organic semiconductor materials. While various mechanisms such as intermolecular exciton-exciton interactions or multilevel intramolecular configurations can generate these BSs, a fundamental understanding of their underlying lattice dynamics remains a key challenge. Within this context, the Merrifield exciton model stands out as a premier framework for capturing the intricate quantum mixing between single-site doubly excited states and two-particle scattering continuum. In this work, by constructing a set of exact two-exciton Bloch states and applying a plane-wave ansatz to treat the resulting inhomogeneous tridiagonal matrices, we provide a complete, rigorous solution to the two-exciton problem in a finite-size Merrifield chain. We analytically map the parameter regions that support two-exciton BSs, proving that at most two distinct types of BSs can emerge, located either above or below the scattering continuum. Furthermore, we provide a quantitative interpretation of how these two types of BSs evolve as a function of the total wave number within the whole Brillouin zone. The obtained closed-form expressions for the eigenenergies and wave functions offer valuable benchmarks for exploring exciton dynamics and optical responses in related molecular aggregates.

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Phys. Rev. B 114, 225127– Published 16 October, 2026
  • Received 20 June 2026
  • Revised 17 September 2026
  • Accepted 5 October 2026
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