Sensitivity of the entanglement spectrum to boundary conditions as a characterization of the phase transition from delocalization to localization

Abstract

Sensitivity of entanglement Hamiltonian spectrum to boundary conditions is considered as a phase detection parameter for delocalized-localized phase transition. By employing one-dimensional models that undergo delocalized-localized phase transition, we study the shift in the entanglement energies and the shift in the entanglement entropy when we change boundary conditions from periodic to anti-periodic. Specifically, we show that both these quantities show a change of several orders of magnitude at the transition point in the models considered. Therefore, this shift can be used to indicate the phase transition points in the models. We also show that both these quantities can be used to determine \emph{mobility edges} separating localized and delocalized states.

6 pages, 5 figures

References in corpus (12)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Entanglement in a second order quantum phase transition
• Entanglement entropy in fermionic Laughlin states
• Entanglement and Quantum Phase Transition Revisited
• Bipartite entanglement entropy in fractional quantum Hall states
• Entanglement in the Majumdar-Ghosh model
• Multi-partite entanglement and quantum phase transition in the one-, two-, and three-dimensional transverse field Ising model
• Dynamics of Global Entanglement under Decoherence
• Signatures of metal-insulator and topological phase transitions in the entanglement of one-dimensional disordered fermions
• Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions
• Scaling of von Neumann entropy at the Anderson transition

Cited by in corpus (5)

• Multi-fractality of the entanglement Hamiltonian eigen-modes
• Characterizing The Many-Body Localization via Studying State Sensitivity to Boundary Conditions
• Single-particle Entanglement of the Entanglement Hamiltonian Eigen-modes
• Directional Localization in Disordered 2D Tight-Binding Systems: Insights from Single Particle Entanglement Measures
• Characterizing the delocalized-localized Anderson phase transition based on the system's response to boundary conditions