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

The entanglement spectrum of a topologically-ordered ground-state that is obtained by partitioning the system under consideration into two subsystems which extend throughout the bulk, has been recently shown to be a probe of the quantum critical behavior of the topological phase at the transition to a direct-product state [1]. Here, we generalize this notion of a bulk entanglement spectrum to extract universal information about disorder-driven topological phase transitions, by performing an extensive, random partition into two subsystems with probability $p\in[0,1]$. We apply our random partitioning procedure to a one-dimensional topological superconductor (TSC), and demonstrate that the phase diagram of the resulting entanglement Hamiltonian describes disorder-driven transitions to a Griffiths phase. [1] T. H. Hsieh and L. Fu, Phys. Rev. Lett. {\bf 113}, 106801 (2014).