Anderson localization and momentum-space entanglement

Abstract

We consider Anderson localization and the associated metal-insulator transition for non-interacting fermions in D = 1, 2 space dimensions in the presence of spatially correlated on-site random potentials. To assess the nature of the wavefunction, we follow a recent proposal to study momentum-space entanglement. For a D = 1 model with long-range disorder correlations, both the entanglement spectrum and the entanglement entropy allow us to clearly distinguish between extended and localized states based upon a single realization of disorder. However, for other models including the D = 2 case with long-range correlated disorder, we find that the method is not similarly successful. We analyze the reasons for its failure, concluding that the much desired generalization to higher dimensions may be problematic.

8 pages, 4 figures. Contribution to J. Stat. Mech. special issue "Quantum Entanglement in Condensed Matter Physics". Minor changes. References added

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Cited by in corpus (17)

• Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions
• Exact Quantum Scars in the Chiral Non-Linear Luttinger Liquid
• Interplay between topology and disorder in a two-dimensional semi-Dirac material
• Anderson Topological Superconductor
• Signatures of metal-insulator and topological phase transitions in the entanglement of one-dimensional disordered fermions
• Universal entanglement spectra in critical spin chains
• Momentum-space entanglement and Loschmidt echo in Luttinger liquids after a quantum quench
• Momentum-space entanglement after a quench in one-dimensional disordered fermionic systems
• Momentum-Space Entanglement in Heisenberg Spin-Half Ladders
• Momentum space entanglement of interacting fermions
• Sensitivity of the entanglement spectrum to boundary conditions as a characterization of the phase transition from delocalization to localization
• Bulk Entanglement Spectrum in Gapped Spin Ladders
• Investigating disordered many-body system with entanglement in momentum space
• Effects of auto-correlated disorder on the dynamics in the vicinity of the many-body localization transition
• Analytic Expression for the Entanglement Entropy of a 2D Topological Superconductor
• Distilling momentum-space entanglement in Luttinger liquids at finite temperature
• Probing Electron Localization and Delocalization in the Selective Long-Range Tight-Binding Model