Preprints

1. Ayral, T., Cancès, E., Faulstich, F. M., Lin, L., & Negre, A. (2026). A quadratic Grassmann manifold optimization problem arising from quantum embedding methods. arXiv:2603.17080.

   arXiv BIB Abstract

   @unpublished{ayral2026grassmann,
     author = {Ayral, Thomas and Cancès, Eric and Faulstich, Fabian M. and Lin, Lin and Negre, Alicia},
     title = {A quadratic Grassmann manifold optimization problem arising from quantum embedding methods},
     note = {arXiv:2603.17080},
     doi = {2603.17080},
     year = {2026}
   }
   

   We analyze mathematical and numerical strategies for minimizing a quadratic function over the Grassmann manifold, J(P) = Tr(BP) - 1/2 Tr(APAP), where A and B are symmetric matrices. Although this non-convex problem typically has multiple local minima, we identify scenarios where a convex auxiliary problem yields the global solution. When this direct approach does not apply, solving the auxiliary problem provides strong initialization for Riemannian optimization and self-consistent field algorithms.

2. Negre, A., Faulstich, F., Kim, R., Ayral, T., Lin, L., & Cancès, E. (2025). New perspectives on Density-Matrix Embedding Theory. arXiv:2503.09881.

   arXiv BIB Abstract

   @unpublished{negre2025dmet,
     author = {Negre, Alicia and Faulstich, Fabian and Kim, Raehyun and Ayral, Thomas and Lin, Lin and Cancès, Eric},
     title = {New perspectives on Density-Matrix Embedding Theory},
     note = {arXiv:2503.09881},
     doi = {2503.09881},
     year = {2025}
   }
   

   Quantum embedding methods enable the study of large, strongly correlated quantum systems by (usually self-consistent) decomposition into computationally manageable subproblems, in the spirit of divide-and-conquer methods. We introduce a generalized DMET framework that relaxes conventional constraints by allowing the low-level descriptor to be an arbitrary one-particle reduced density matrix (1-RDM), with bath construction based on optimizing a quantitative criterion related to maximal disentanglement between different fragments.

Refereed Journal Articles

1. Negre, A., Mathevet, R., Chalopin, B., & Massenot, S. (2023). Unexpected optimal measurement protocols in Bell’s inequality violation experiments. American Journal of Physics, 91(1), 64–73. https://hal.sorbonne-universite.fr/LCAR_FEM/hal-03943241v1

   DOI HAL BIB

   @article{negre2023bell,
     author = {Negre, Alicia and Mathevet, Renaud and Chalopin, Benoît and Massenot, Sébastien},
     title = {Unexpected optimal measurement protocols in Bell's inequality violation experiments},
     journal = {American Journal of Physics},
     publisher = {American Association of Physics Teachers},
     volume = {91},
     number = {1},
     pages = {64-73},
     year = {2023},
     month = jan,
     doi = {10.1119/5.0102516},
     url = {https://hal.sorbonne-universite.fr/LCAR_FEM/hal-03943241v1}
   }
   

Refereed Conference Proceedings