Nonergodicity of entanglement and its complementary behavior to   magnetization in infinite spin chain
  We consider the problem of the validity of a statistical mechanical description of two-site entanglement in an infinite spin chain described by the XY model Hamiltonian. We show that the two-site entanglement of the state, evolved from the initial equilibrium state, after a change of the magnetic field, does not approach its equilibrium value. This suggests that two-site entanglement, like (single-site) magnetization, is a nonergodic quantity in this model. Moreover we show that these two nonergodic quantities behave in a complementary way. 
Aditi Sen De, Ujjwal Sen, Maciej Lewenstein