The Anderson Orthogonality Catastrophe as a Quantum Phase Transition
Anderson Orthogonality Catastrophe, Universality, Quantum Phase Transition.
In the thermodynamic limit, two gases of confined non-interacting fermions at zero temperature, which differ only by the presence of a local impurity or by a symmetrical potential that decays rapidly with distance, have equal energy densities. In the same limit, their respective ground states, as a consequence of the Anderson Orthogonality Catastrophe, are orthogonal. We study this phenomenology, demonstrate its universality, and develop its analogy with the First Order Quantum Phase Transition.