Bulk-Edge Correspondence in Fractional Quantum Hall States

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.

6 pages, 4 figures

References in corpus (10)

• Non-Abelian Anyons and Topological Quantum Computation
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Ground state entanglement and geometric entropy in the Kitaev's model
• Entanglement entropy in fermionic Laughlin states
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Bipartite entanglement entropy in fractional quantum Hall states
• Bulk-boundary correspondence in (3+1)-dimensional topological phases
• Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality
• Edge--Entanglement correspondence for gapped topological phases with symmetry
• Universal edge information from wave-function deformation

Cited by in corpus (7)

• Entanglement spectroscopy of non-Abelian anyons: Reading off quantum dimensions of individual anyons
• Statistical interactions and boson-anyon duality in fractional quantum Hall fluids
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Entanglement Action for the Real-Space Entanglement Spectra of Composite Fermion Wave Functions
• Intercomponent entanglement entropy and spectrum in binary Bose-Einstein condensates
• Analytic bulk-edge connection in circular-symmetric models
• Bisognano-Wichmann Hamiltonian for the entanglement spectroscopy of fractional quantum Hall states