Edge States Effects in Quantum Work Statistics

Motivated by the objective of quantifying the energetic cost of accessing boundary phases through local control, we investigate here a simple, analytically tractable quantum impurity model. This model exhibits a rich boundary phase diagram, characterized by phases with different numbers of edge states. By considering a local quench protocol that drives the system out of equilibrium, we calculate exactly the resulting quantum work distribution across these phases. Our results show that the presence of edge states strongly alters this distribution. In particular, we analytically determine key fingerprints of these states both near the low-energy threshold and in the high-energy region.