CE30 - Physique de la matière condensée et de la matière diluée

Large-order diagrammatic computations for strongly correlated fermions – LODIS

Submission summary

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. Here we propose to develop and use an approach that works directly in the thermodynamic limit. The idea is to expand physical quantities into connected Feynman diagrams,
to evaluate all diagrams up to a maximal expansion order using an efficient Monte Carlo algorithm, and to extrapolate to the infinite order limit, if necessary after applying a divergent-series resummation method. The project focuses on two textbook models: the Hubbard model, which accurately describes cold atoms in optical lattices and is also relevant to materials, and the resonant-gas model, which accurately described cold atoms near a Feshbach resonance and is also relevant to neutron matter. For the Hubbard model, in 3D and 2D on the cubic and square lattices, we will study broken-symmetry phases. We will determine the phase diagram, which is expected to host several competing phases: for attractive interactions in the polarized regime, a conventional superfluid phase, a breached-pair phase and FFLO phases; and for repulsive interactions in the doped regime, a conventional antiferromagnetic phase and striped phases. For the resonant gas, we will investigate the physical properties of the normal phase in 3D, by computing key experimentally accessible quantities, in the different regimes of temperature, polarization, and interaction strength: equation of state and contact parameter, momentum distribution and off-diagonal pair correlation function, single-particle spectral function and Raman spectra, and multi-body density correlation functions. Our data will serve as benchmarks for ultracold atom experiments in the near future. The methods to be developed in this project will also be applicable to condensed matter and nuclear physics.

Project coordination

Félix Werner (Laboratoire Kastler Brossel)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

LKB Laboratoire Kastler Brossel
LPENS Laboratoire de physique de l'ENS

Help of the ANR 313,980 euros
Beginning and duration of the scientific project: August 2022 - 48 Months

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