Ecole Normale Supérieure, Laboratoire Kastler Brossel

Position ID:ENS-Laboratoire Kastler Brossel-POSTDOC [#23962]
Position Title: Postdoc: Diagrammatic Monte Carlo study of high-temperature superconductivity
Position Type:Postdoctoral
Position Location:Paris, Paris 75005, France [map] sort by distance
Subject Areas: Physics / Computational physics, Condensed Matter Theory, Quantum Field Theory, Quantum magnetism, quantum phase transitions, Statistical physics, Superconductivity
Appl Deadline:2023/01/03 11:59PMhelp popup deleted
Position Description:    

*** this position has been closed and new applications are no longer accepted. ***

Strongly correlated fermions are ubiquitous in various contexts: electrons in solids or molecules, nucleons in nuclei or neutron stars, quarks in QCD... Our understanding of such systems is limited by the difficulty to compute their properties in a reliable and unbiased way. For conventional Quantum Monte Carlo methods, the computational time generically grows exponentially with the number of fermions (due to the “fermion sign problem”); typically, one resorts to uncontrolled approximations in order to avoid this problem. The situation is fundamentally different with diagrammatic Monte Carlo approaches that work directly in the thermodynamic limit. The idea is to expand physical quantities into connected Feynman diagrams, evaluate all diagrams up to a maximal expansion order using an efficient Monte Carlo algorithm, and extrapolate to the infinite-order limit (if necessary after applying a divergent-series resummation method).

We have recently reported the first diagrammatic Monte Carlo results in a superconducting phase [1]. We studied the Hubbard model with attractive interactions, implementing spontaneous symmetry breaking by expanding around a BCS Hamiltonian. Thanks to the connected determinant algorithm [2] generalized to anomalous propagators, we could sum all connected Feynman diagrams up to 12 loops. Our study includes the case of a polarizing Zeeman field, where unbiased benchmarks are unavailable due to the fermion sign problem. At low temperature, we observe a first-order superfluid-to-normal transition; compared to mean-field theory, our results agree qualitatively, but quantitatively the deviations can be very large. Conceptually, we found that diagrammatic series in superconducting phases are governed, at large order, by the long-wavelength thermal fluctuations of the Goldstone mode, which reduces the convergence rate of the series, without causing a divergence. We also understood that the method works in metastable phases, where a divergence of the series only appears at very large orders.

We plan to extend this approach to repulsive interactions, where one expects a competition between d-wave superconductivity and antiferromagnetic stripes. Our approach offers the opportunity to provide reliable answers to major long-standing open problems of direct relevance to high-temperature superconductivity in cuprates.

[1] G. Spada, R. Rossi, F. Simkovic, R. Garioud, M. Ferrero, K. Van Houcke, F. Werner, arXiv:2103.12038

[2] R. Rossi, PRL 119, 045701 (2017) [arXiv:1612.05184]

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