Séminaire du LPTMS: Kris Van Houcke


11:00 - 12:30

LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay
15 Rue Georges Clemenceau, Orsay, 91405

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Summation of diagrammatic series for a strongly correlated fermionic theory with zero convergence radius

Kris Van Houcke (École Normale Supérieure, Paris)

In this talk I will mainly focus on the unitary Fermi gas (spin 1/2 fermions with contact interactions in 3D, which describes cold atomic gases at a Feshbach resonance) in the normal phase. Thanks to a diagrammatic Monte Carlo algorithm, we accurately sample all skeleton
diagrams (built on dressed single-particle and pair propagators) up to order nine [1]. The diagrammatic series is divergent and there is no small parameter so that a resummation method is needed. We compute the large-order asymptotics of the diagrammatic series, based on a functional integral representation of the skeleton series and the saddle-point
method. We show that the radius of convergence is actually zero, but the series is still resummable, by a generalised conformal-Borel transformation that incorporates the large-order asymptotics [2]. This yields new high-precision data, not only for the equation of state, but also for Tan’s contact coefficient and for the momentum distribution [3].
I will also highlight some recent developments in (determinant) diagrammatic Monte Carlo and present new high-precision data for the Fermi polaron, which is a single impurity atom immersed in a Fermi sea.


[1] K. Van Houcke, F. Werner, T. Ohgoe, N. V. Prokof’ev, and B. V. Svistunov, « Diagrammatic Monte Carlo algorithm for the resonant Fermi gas », Phys. Rev. B 99, 035140 (2019).
[2] R. Rossi, T. Ohgoe, K. Van Houcke, F. Werner, « Resummation of diagrammatic series with zero convergence radius for strongly correlated fermions », Phys. Rev. Lett. 121, 130405 (2018)
[3] R. Rossi, T. Ohgoe, E. Kozik, N. Prokof’ev, B. Svistunov, K. Van Houcke, F. Werner, « Contact and momentum distribution of the unitary Fermi gas », Phys. Rev. Lett. 121, 130406 (2018)

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