Weak coupling limit for the ground state energy of the 2D Fermi polaron

Abstract

We analyze the ground state energy for N fermions in a two-dimensional box interacting with an impurity particle via two-body point interactions. We allow for mass ratios M > 1.225 between the impurity mass and the mass of a fermion and consider arbitrarily large box sizes while keeping the Fermi energy fixed. Our main result shows that the ground state energy in the limit of weak coupling is given by the polaron energy. The polaron energy is an energy estimate based on trial states up to first order in particle-hole expansion, which was proposed by Chevy in the physics literature. For the proof we apply a Birman-Schwinger principle that was recently obtained by Griesemer and Linden. One main new ingredient is a suitable localization of the polaron energy.

References in corpus (16)

• Universal phase diagram of a strongly interacting Fermi gas with unbalanced spin populations
• Fermi-Polaron: Diagrammatic Monte Carlo for Divergent Sign-Alternating Series
• Polaron to molecule transition in a strongly imbalanced Fermi gas
• Normal state of highly polarized Fermi gases: Full many-body treatment
• Fermi polarons in two dimensions
• Rotation of quantum impurities in the presence of a many-body environment
• Polaron-molecule transitions in a two-dimensional Fermi gas
• Highly polarized Fermi gases in two dimensions
• Ground state of a tightly bound composite dimer immersed in a Fermi Sea
• Decay of polarons and molecules in a strongly polarized Fermi gas
• Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions
• Multiparticle Schrodinger operators with point interactions in the plane
• New theoretical approaches to Bose polarons
• Spectral Theory of the Fermi Polaron
• Stability of the two-dimensional Fermi polaron
• Energy contribution of a point interacting impurity in a Fermi gas