A formally exact real-space representation of the Berry phase on infinite lattices: Applications to dipole and quadrupole moments

Y. Onaya; F. Hamano; T. Fukui

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arXiv · 2503.16897

A formally exact real-space representation of the Berry phase on infinite lattices: Applications to dipole and quadrupole moments

Y. Onaya·F. Hamano·T. Fukui

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Abstract

Inspired by Kitaev's real-space representation of Chern numbers, we develop a real-space formulation of the Berry phase for infinite lattices. While the well-known Resta formula for the Berry phase is defined under periodic boundary conditions for finite lattices, our approach constructs the Berry phase directly on an infinite lattice without requiring momentum-space discretization. We apply this method to several disordered models to examine its validity. Furthermore, we attempt to generalize the real-space representation to the quadrupole moment, drawing an analogy to the generalization of the Resta formula for the quadrupole moment.

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Y. Onaya, F. Hamano, T. Fukui. 2025-03-21. A formally exact real-space representation of the Berry phase on infinite lattices: Applications to dipole and quadrupole moments. https://arxiv.org/abs/2503.16897

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