How to Cite

If you use TENSO in your research, please cite the following papers. Citation formats are provided in BibTeX, APA, and ACS styles.

TENSO software package

Rodriguez Betancourt, J. C., Anderson, M. C., Niu, L., Chen, X. & Franco, I.
TENSO: Software Package for Numerically Exact Open Quantum Dynamics Based on Efficient Tree Tensor Network Decomposition of the Hierarchical Equations of Motion.
arXiv:2603.17711 (2026).

This paper describes the TENSO software package for simulating open quantum dynamics in structured thermal environments using tree tensor network decomposition of the HEOM.

@misc{rodriguez2026tenso,
  author        = {Rodriguez Betancourt, Juan C. and Anderson, Michelle C. and
                   Niu, Luchang and Chen, Xinxian and Franco, Ignacio},
  title         = {{TENSO}: Software Package for Numerically Exact Open Quantum
                   Dynamics Based on Efficient Tree Tensor Network Decomposition
                   of the Hierarchical Equations of Motion},
  year          = {2026},
  eprint        = {2603.17711},
  archivePrefix = {arXiv},
  primaryClass  = {physics.chem-ph},
  doi           = {10.48550/arXiv.2603.17711}
}

Primary reference — TTN-HEOM and TENSO

Chen, X. & Franco, I.
Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments.
J. Chem. Phys. 163, 104109 (2025).

This paper introduces the TTN-HEOM method, derives the TDVP-based master equations for all core tensors, describes the three propagation strategies (direct integration VMF, fixed-rank PS1, adaptive-rank PS2), and presents the TENSO implementation.

@article{chen2025ttnheom,
  author  = {Chen, Xinxian and Franco, Ignacio},
  title   = {Tree tensor network hierarchical equations of motion based on
             time-dependent variational principle for efficient open quantum
             dynamics in structured thermal environments},
  journal = {J. Chem. Phys.},
  volume  = {163},
  pages   = {104109},
  year    = {2025},
  doi     = {10.1063/5.0278591}
}

Bexcitonics — theoretical foundation

Chen, X. & Franco, I.
Bexcitonics: Quasiparticle approach to open quantum dynamics.
J. Chem. Phys. 160, 204116 (2024).

This paper develops the bexcitonic quasiparticle picture that underlies the HEOM generalization used in TENSO. It demonstrates that all HEOM variants share a common bexcitonic structure parameterized by the choice of metric and representation.

@article{chen2024bexcitonics,
  author  = {Chen, Xinxian and Franco, Ignacio},
  title   = {Bexcitonics: Quasiparticle approach to open quantum dynamics},
  journal = {J. Chem. Phys.},
  volume  = {160},
  pages   = {204116},
  year    = {2024},
  doi     = {10.1063/5.0198567}
}

Funding acknowledgment