Correspondence between entanglement spectrum and energy excitations
Using exact diagonalization for non-interacting systems and density matrix renormalization group for interacting systems we show that Li and Haldane’s conjecture  on the correspondence between the low-lying many-particle excitation spectrum and the entanglement spectrum holds for disordered ballistic one-dimensional many-particle systems. We observe and explain the presence of an unexpected shell structure in the excitation spectrum . The low-lying shells are robust and survive even for strong electron-electron interactions.
 Li H. and Haldane F. D. M., Phys. Rev. Lett., 101(2008) 010504.
 S. Leiman, A. Eisenbach and R. Berkovits, EPL, 112 (2015).