Entanglement, subsystem particle numbers and topology in free fermion   systems
  We study the relationship between bipartite entanglement, subsystem particle number and topology in a half-filled free fermion system. It is proposed that the spin-projected particle numbers can distinguish the quantum spin Hall state from other states, and can be used to establish a new topological index for the system. Furthermore, we apply the new topological invariant to a disordered system and show that a topological phase transition occurs when the disorder strength is increased beyond a critical value. It is also shown that the subsystem particle number fluctuation displays behavior very similar to that of the entanglement entropy. This provides a lower-bound estimation for the entanglement entropy, which can be utilized to obtain an estimate of the entanglement entropy experimentally. 
Y. F. Zhang, L. Sheng, R. Shen, Rui Wang, D. Y. Xing
cond-mat.mes-hall cond-mat.stat-mech