Bulk-Edge Correspondence in Fractional Quantum Hall States

TL;DR

This paper confirms the bulk-edge correspondence in fractional quantum Hall states by showing that the entanglement spectrum's universal part contains only edge excitations, enabling extraction of full edge information from the ground state.

Contribution

It provides a rigorous verification that the entanglement spectrum's universal part corresponds exactly to the edge excitations in fractional quantum Hall systems.

Findings

Eigenstates in the universal entanglement spectrum are pure edge excitations.

Entanglement spectrum levels match the eigenenergies of an effective edge Hamiltonian.

Full edge excitation information can be obtained from the subsystem's reduced ground state.

Abstract

We substantiate a complete picture of the "bulk-edge correspondence" conjecture for topological phases. By studying the eigenstates in the entanglement spectrum for both the ideal and realistic Coulomb ground state of the fractional quantum Hall system, it is verified that the eigenstates in the universal part of the entanglement spectrum purely lie in the Hilbert space of the edge excitations projected onto the physical Hilbert space of the subsystem itself. Hence, not only are the eigenlevels in the entanglement spectrum in one-to-one correspondence with the eigenenergies of an effective dynamical edge Hamiltonian, but all the eigenstates are confirmed to be the actual (projected) edge excitations of the subsystem. This result also reveals the possibility of extracting the full information of the edge excitations from the state of the subsystem reduced from a geometric cut of the pure ground state of the total system in topological phases.