Quantum information measures for lattice fermions in a harmonic trap

We study spinless fermions in a one-dimensional lattice in the presence of a harmonic trap from the perspective of quantum information measures. In the ground state, the system undergoes a local quantum phase transition upon increasing the particle number, which is the result of the formation of a local band insulator in the center of the trap. We show that the bipartite entanglement entropy can be used as an order parameter to characterize the transition. We also study excited eigenstates by calculating the average von Neumann and second Renyi entropies, and compare results to the thermodynamic entropy and the mutual information of mixed states at the same energy density. While the thermodynamic entropy exhibits a peak at the critical point, other quantities decrease with increasing the particle number and, at low temperatures, vanish close to the critical point. Experiments with ultracold atoms on optical lattices may therefore detect the local quantum phase transition by measuring the second Renyi entropy.