Rammelmüller, Lukas - LMU Munich

Approaching a Quantum Phase Transition one Atom at a Time

Experiments with only a few individual atoms allow us to shed light on the crossover from few- to many-body physics. In this spirit, we investigate a few-body counterpart of the well-studied phenomenon of a magnetic impurity in the vicinity of an s -wave superconductor. Already for few particles we find a ground-state level crossing between a non-magnetic and a magnetic sector, which corresponds to a fermion-parity changing sharp quantum phase transition. This transition occurs as the impurity strength is increased while the fermions interact attractively and can be explained by the tendency of the system to form a single-particle gap due to pair formation. We obtain numerically sound results by exactly solving the problem with FCI in a truncated Hilbert space. To improve convergence we exploit a trick known in the nuclear theory community, namely the use of an effective potential, which essentially constitutes a particularly effective renormalization procedure allowing us to more efficiently obtain physical observables free from a cutoff dependence.