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

TL;DR

This paper demonstrates that the conjectured link between many-particle excitation spectra and entanglement spectra applies to disordered ballistic 1D systems, revealing a robust shell structure unaffected by interactions.

Contribution

It develops an efficient method to compute the entanglement spectrum of low-energy excitations and confirms the conjecture in disordered, interacting, and non-interacting 1D systems.

Findings

The correspondence holds in disordered ballistic 1D systems.

An unexpected shell structure in excitation spectra is observed.

Shell structure persists under strong electron-electron interactions.

Abstract

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 computational efficient way to calculate the ES of low-excitation of non-interacting systems. We observe and explain the presence of an unexpected shell structure in the excitation structure. The low-lying shell are robust and survive even for strong electron-electron interactions.