Mediated Interactions between Fermi Polarons in the Strongly Interacting Regime

Mediated interactions between quasiparticles lie at the heart of Landau Fermi-liquid theory, yet their behavior in the strongly correlated regime is not fully understood. Motivated by recent experiments [Nat. Phys. 20, 68--73 (2024)], we investigate mediated interactions between quasiparticles emerging from a Fermi sea---Fermi polarons---using zero-temperature quantum Monte Carlo methods. Our main result is that the Landau interaction between polarons remains repulsive in the strongly interacting regime for any coupling strength in the polaronic branch, in contrast to the downward trend observed experimentally near resonance. Deep in the short-range universal regime, our results are insensitive to the microscopic details of the interaction potential, providing robust evidence for the sign of the ground-state induced interaction. In addition, we determine the real-space interaction between static impurities, recovering a Ruderman-Kittel-Kasuya-Yosida (RKKY)-like behavior at weak coupling and the nonperturbative Born-Oppenheimer result at strong coupling. More broadly, our results establish a microscopic benchmark for how Landau quasiparticle interactions survive beyond the perturbative regime of strongly correlated quantum matter.