Interaction induced flattening of optical transition quantum geometry
Abstract
The Riemannian geometry of optical transition dipoles has become a useful picture for understanding linear and nonlinear optical response. Here we argue that the interacting quantum geometry of optical transitions possesses a rich structure and can be naturally delineated into two types: localized and delocalized particle-hole excitations. The former possess uniform quantum geometry with flat (vanishing) Hermitian curvature; the latter possess non-uniform quantum geometry with non-vanishing Hermitian curvature. As a striking example, we find that uniform quantum geometry can be produced by electron-hole interactions: even when composed from extended Bloch states in the particle and hole bands, we find excitons have uniform and flat quantum geometry. By developing a many-body length gauge formulation of nonlinear response, we find this uniform and flat excitonic quantum geometry zeros its third-order circular photoconductivity in non-magnetic materials in stark contrast to its non-interacting counterparts. Similarly, the zero Hermitian curvature of localized optical transitions locks their Hall response to that of the ground state. This demonstrates the rich landscape of many-body optical response controlled by an interacting quantum geometry.
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BibTeX
@misc{yang2026interaction,
title = {{Interaction induced flattening of optical transition quantum geometry}},
author = {Xu Yang and Justin C. W. Song},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28642},
eprint = {2609.28642},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28642},
}
RIS
TY - UNPB
TI - Interaction induced flattening of optical transition quantum geometry
AU - Xu Yang
AU - Justin C. W. Song
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28642
UR - https://arxiv.org/abs/2609.28642
AB - The Riemannian geometry of optical transition dipoles has become a useful picture for understanding linear and nonlinear optical response. Here we argue that the interacting quantum geometry of optical transitions possesses a rich structure and can be naturally delineated into two types: localized and delocalized particle-hole excitations. The former possess uniform quantum geometry with flat (vanishing) Hermitian curvature; the latter possess non-uniform quantum geometry with non-vanishing Hermitian curvature. As a striking example, we find that uniform quantum geometry can be produced by electron-hole interactions: even when composed from extended Bloch states in the particle and hole bands, we find excitons have uniform and flat quantum geometry. By developing a many-body length gauge formulation of nonlinear response, we find this uniform and flat excitonic quantum geometry zeros its third-order circular photoconductivity in non-magnetic materials in stark contrast to its non-interacting counterparts. Similarly, the zero Hermitian curvature of localized optical transitions locks their Hall response to that of the ground state. This demonstrates the rich landscape of many-body optical response controlled by an interacting quantum geometry.
ER -