Correspondence between many-particle excitations and the entanglement spectrum of disordered ballistic one-dimensional systems

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. In order to demonstrate the correspondence we develop a computationally efficient way to calculate the entanglement spectrum of low-lying excitation of non-interacting 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.