Many-body multipole index and bulk-boundary correspondence

TL;DR

This paper introduces new many-body multipole indices for interacting insulators with point group symmetries, enabling clear identification of nontrivial multipolar states and establishing a bulk-boundary correspondence.

Contribution

It proposes symmetry-compatible multipole indices that are quantized and effective as order parameters, linking bulk properties to boundary states in interacting systems.

Findings

Indices are quantized and commute with Hamiltonian under symmetry.

Non-zero indices indicate the presence of edge or corner states.

Effective as order parameters in representative models.

Abstract

We propose new dipole and quadrupole indices for interacting insulators with point group symmetries. The proposed indices are defined in terms of many-body quantum multipole operators combined with the generator of the point group symmetry. Unlike the original multipole operators, these combined operators commute with Hamiltonian under the symmetry and therefore their eigenvalues are quantized. This enables a clear identification of nontrivial multipolar states. We calculate the multipole indices in representative models and show their effectiveness as order parameters. Furthermore, we demonstrate a bulk-boundary correspondence: a non-zero index implies the existence of edge/corner states under the the point group symmetry.