Heidelberg Framework Links Fermi Polaron Quasiparticles to Anderson Orthogonality Catastrophe via Residual Impurity Motion

The work resolves a decades-old partition in quantum many-body theory by demonstrating that the two regimes are limiting cases of one Hamiltonian rather than fundamentally incompatible pictures. Using a combination of diagrammatic resummation and renormalization-group flow equations, the authors track how the impurity’s recoil energy, even when parametrically small, cuts off the infrared divergence that otherwise destroys quasiparticle weight. This yields a continuous crossover between a well-defined Fermi polaron at moderate mass ratios and an orthogonality-catastrophe ground state only in the strict infinite-mass limit.

Because the same formalism recovers both the known polaron-molecule transition and the orthogonality overlap catastrophe as different regimes of a single parameter, it supplies a quantitative bridge between ultracold-atom experiments and solid-state impurity problems. The theory further predicts that the emergent energy gap scales as the square root of the impurity recoil energy, a relation directly testable by radio-frequency spectroscopy in two-dimensional Fermi gases.

The advance matters beyond impurity physics because any candidate unification of quantum mechanics with gravity must ultimately reconcile mobile and frozen degrees of freedom; the present construction offers a concrete, experimentally anchored example of how an ostensibly classical limit can still support coherent quasiparticle excitations. Future measurements in twisted bilayer graphene or transition-metal dichalcogenides can therefore serve as analog gravity laboratories.

Next steps include embedding the framework into dynamical mean-field calculations for lattice models and extending it to non-equilibrium quenches, both of which are already under way in the ISOQUANT collaboration.