Entanglement Signatures of Multipolar Higher Order Topological Phases

TL;DR

This paper introduces a method to identify multipolar higher-order topological phases in free-fermion and interacting systems by analyzing their nested entanglement Hamiltonians, revealing characteristic spectral degeneracies.

Contribution

The authors develop a novel nested entanglement Hamiltonian approach to characterize multipolar higher-order topological phases, applicable to both free-fermion and interacting systems.

Findings

Successfully identifies higher-order topological phases via entanglement spectrum degeneracies.

Computes nested entanglement spectra for fermionic and bosonic multipole phases.

Demonstrates the method's effectiveness in classifying complex topological phases.

Abstract

We propose a procedure that characterizes free-fermion or interacting multipolar higher-order topological phases via their bulk entanglement structure. To this end, we construct nested entanglement Hamiltonians by first applying an entanglement cut to the ordinary many-body ground state, and then iterating the procedure by applying further entanglement cuts to the (assumed unique) ground state of the entanglement Hamiltonian. We argue that an $n$-th order multipolar topological phase can be characterized by the features of its $n$-th order nested entanglement Hamiltonian e.g., degeneracy in the entanglement spectrum. We explicitly compute nested entanglement spectra for a set of higher-order fermionic and bosonic multipole phases and show that our method successfully identifies such phases.