Research

My research is interested in the mathematics of interacting quantum systems.

During my PhD, I have been focusing on two approximations methods dealing with fermions : the Density Matrix Embedding Theory (DMET) and the Dynamical Mean-Field Theory (DMFT), which allow to compute efficiently reduced quantities such as the one-particle reduced density matrix (DMET) or the quantum one-body Green’s function (DMFT).

These approximations belong to the general class of embedding methods, whose general philosophy is based on a “decomposition” of the one-particle Hilbert space into “fragments” (a.k.a. “clusters”). For each of them, one defines an interacting but smaller subsystem, whose parameters are determined by a global self-consistent equation.

The purpose of these methods is to alleviate the curse of dimensionality associated with interacting quantum systems, and to describe quantitatively interaction driven effects such as the metal-to-insulator Mott transition in the Fermi-Hubbard model.

Preprints

• Cancès, É., Kirsch, A., & Perrin-Roussel, S. (2024). A mathematical analysis of IPT-DMFT. arXiv preprint arXiv:2406.03384.
• Cancès, É., Faulstich, F. M., Kirsch, A., Letournel, E., & Levitt, A. (2023). Some mathematical insights on density matrix embedding theory. arXiv preprint arXiv:2305.16472, accepted in Communications in Pure and Applied Mathematics (CPAM).

Publications

• Schäfer, T., Wentzell, N., Šimkovic IV, F., He, Y. Y., Hille, C., Klett, M., … & Georges, A. (2021). Tracking the footprints of spin fluctuations: A multimethod, multimessenger study of the two-dimensional Hubbard model. Physical Review X, 11(1), 011058.