Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Chen, Lei, Ghorashi, Sayed Ali Akbar, Cano, Jennifer, Crépel, Valentin
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866912978074337280
author Chen, Lei
Ghorashi, Sayed Ali Akbar
Cano, Jennifer
Crépel, Valentin
author_facet Chen, Lei
Ghorashi, Sayed Ali Akbar
Cano, Jennifer
Crépel, Valentin
contents Robust flavor-polarized phases are a striking hallmark of many flat-band moiré materials. In this work, we trace the origin of this spontaneous polarization to a lesser-known quantum-geometric quantity: the quantum-geometric dipole. Analogous to how the quantum metric governs the spatial spread of wavepackets, we show that the quantum-geometric dipole sets the characteristic size of particle-hole excitations, e.g. magnons in a ferromagnet, which in turn boosts their gap and stiffness. Indeed, the larger the particle-hole separation, the weaker the mutual attraction, and the stronger the excitation energy. In topological bands, this energy enhancement admits a lower bound within the local-mode approximation, highlighting the crucial role of topology in flat-band ferromagnetism. We illustrate these effects in microscopic models, emphasizing their generality and relevance to moiré materials. Our results establish the quantum-geometric dipole as a predictive geometric indicator for ferromagnetism in flat bands, a crucial prerequisite for topological order.
format Preprint
id arxiv_https___arxiv_org_abs_2506_22417
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands
Chen, Lei
Ghorashi, Sayed Ali Akbar
Cano, Jennifer
Crépel, Valentin
Mesoscale and Nanoscale Physics
Materials Science
Strongly Correlated Electrons
Robust flavor-polarized phases are a striking hallmark of many flat-band moiré materials. In this work, we trace the origin of this spontaneous polarization to a lesser-known quantum-geometric quantity: the quantum-geometric dipole. Analogous to how the quantum metric governs the spatial spread of wavepackets, we show that the quantum-geometric dipole sets the characteristic size of particle-hole excitations, e.g. magnons in a ferromagnet, which in turn boosts their gap and stiffness. Indeed, the larger the particle-hole separation, the weaker the mutual attraction, and the stronger the excitation energy. In topological bands, this energy enhancement admits a lower bound within the local-mode approximation, highlighting the crucial role of topology in flat-band ferromagnetism. We illustrate these effects in microscopic models, emphasizing their generality and relevance to moiré materials. Our results establish the quantum-geometric dipole as a predictive geometric indicator for ferromagnetism in flat bands, a crucial prerequisite for topological order.
title Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands
topic Mesoscale and Nanoscale Physics
Materials Science
Strongly Correlated Electrons
url https://arxiv.org/abs/2506.22417