Entanglement Spectrum of a Random Partition: Connection with the Localization Transition

Abstract

We study the entanglement spectrum of a translationally-invariant lattice system under a random partition, implemented by choosing each site to be in one subsystem with probability $p\in [0,1]$. We apply this random partitioning to a translationally-invariant (i.e., clean) topological state, and argue on general grounds that the corresponding entanglement spectrum captures the universal behavior about its disorder-driven transition to a trivial localized phase. Specifically, as a function of the partitioning probability $p$, the entanglement Hamiltonian $H_A$ must go through a topological phase transition driven by the percolation of a random network of edge-states. As an example, we analytically derive the entanglement Hamiltonian for a one-dimensional topological superconductor under a random partition, and demonstrate that its phase diagram includes transitions between Griffiths phases.

4 pages, 2 figures, 3 pages of Supplementary Material

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• Numerical investigations of the extensive entanglement Hamiltonian in quantum spin ladders
• Analytic Expression for the Entanglement Entropy of a 2D Topological Superconductor
• Entanglement entropy of XX spin $1/2$ chain with random partitioning at arbitrary temperature
• Distribution of entanglement Hamiltonian spectrum in free fermion models
• Refined Characterization of Lattice Chern Insulators by Bulk Entanglement Spectrum