Theory of Dipole Insulators

TL;DR

This paper extends the concept of insulators to systems with conserved dipole moments, introducing multipolar insulators and developing criteria to distinguish phases based on dipole localization and stiffness.

Contribution

It introduces a universal framework for identifying multipolar insulators, focusing on dipole moments, and relates these to many-body quadrupole operators and phase transitions.

Findings

Defined dipole and multipolar insulators.

Established criteria for phase distinction based on dipole localization.

Illustrated concepts with exactly solvable models.

Abstract

Insulating systems are characterized by their insensitivity to twisted boundary conditions as quantified by the charge stiffness and charge localization length. The latter quantity was shown to be related to the expectation value of the many-body position operator and serves as a universal criterion to distinguish between metals and insulators. In this work we extend these concepts to a new class of quantum systems having conserved charge and dipole moments. We refine the concept of a charge insulator by introducing notions of multipolar insulators, e.g., a charge insulator could be a dipole insulator or dipole metal. We develop a universal criterion to distinguish between these phases by extending the concept of charge stiffness and localization to analogous versions for multipole moments, but with our focus on dipoles. We are able relate the dipole localization scale to the expectation value of a recently introduced many-body quadrupole operator. This refined structure allows for the identification of phase transitions where charge remains localized but, e.g., dipoles delocalize. We illustrate the proposed criterion using several exactly solvable models that exemplify these concepts, and discuss a possible realization in cold-atom systems.