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Félix Werner

Diagrammatic Monte Carlo

We develop Monte Carlo methods to sum all connected Feynman diagrams to high orders, and to extract the values of physical quantities up to a controlled error. For the unitary Fermi gas, we found that the series has zero convergence radius, and is nevertheless resummable by a generalized Borel transformation [Rossi et al., PRL 2018]. Our results for the two-body contact parameter C2 [Rossi et al., PRL 2018] were confirmed by subsequent experiments at MIT and Swinburne. More recently we have extended the method to superconducting phases, by expanding around BCS hamiltonians for the attractive Hubbard model [Spada et al., arXiv].

Example of diagram taken into account in our computation for the unitary Fermi gas. The lines represent single-particle propagators while the rectangles represent pair-propagators.

Three-body contact for fermions

We introduced the concept of three-body contact C3 for equal-mass two-component fermions with resonant short-range interactions. If one measures the positions of all particles, the number of triplets whose r.m.s. interparticle separation is smaller than ε scales as C3 * ε5.5454485 . We derived several other relations involving C3 , including an expression of the three-body loss rate in terms of C3 * Im(a3), where a3 is a “3-body parameter” defined through the asymptotic behavior of the 3-body wavefunction at distances intermediate between the range and the two-body scattering length [Werner and Leyronas, CR Phys 2024].

Geometric illustration of the three-body loss process. The total decay rate is given
by the probability flux exiting from the grey region. It is dominated by the flux through the green circular arcs, which corresponds to three-body losses. The blue
arrows represent the deep-dimer + atom outgoing wave, corresponding to a deeply bound dimer and an atom flying apart with a large relative momentum and escaping from the trap. [For the purpose of making this illustrative drawing two-dimensional, we considered N=3 particles in one space dimension, and fixed the center-of-mass coordinate to the origin. The positions of the three particles are then determined by the Jacobi coordinates r and ρ. The trapping region was simply assumed to be a symmetric interval around the origin.]

Personal homepage

Current postdoc: Nils Caci (since 2023)
Former postdoc: Gabriele Spada (2018-2020)
Former student: Riccardo Rossi (2014-2017, co-advised with Kris Van Houcke)

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