Flat-band systems: A platform to realize the moments of Quantum Metric
Abstract
The quantum metric is a fundamental geometric property of Bloch bands that governs a wide range of physical phenomena, yet experimentally accessing it remains challenging. We show that the momentum-space variation of the quantum metric can be probed through the real-space dynamics of a Gaussian wave packet prepared in an isolated flat band. Following the application of a weak constant force, we demonstrate analytically that the leading order change in the wave-packet variance is linear in time and contains a contribution proportional to the wave-packet averaged gradient of the quantum-metric trace. This geometric contribution remains finite despite the absence of band dispersion. We illustrate the effect using a gapped Lieb lattice with an exactly flat middle band and vanishing Berry curvature, allowing the quantum-metric contribution to the spreading to be isolated. The numerical results agree with the analytical prediction and confirm the quantum-metric contribution to the wave-packet spreading. The required lattice preparation, tunable hopping amplitudes, applied force, and density measurements are compatible with established ultracold-atom techniques, providing a possible platform for observing the predicted response. Our results establish wave-packet spreading as a dynamical probe of quantum geometry in flat-band systems.
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BibTeX
@misc{gangadhar2026flatband,
title = {{Flat-band systems: A platform to realize the moments of Quantum Metric}},
author = {Rishi Gangadhar and Binayyak Roy and Vito Scarola and Sumanta Tewari},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08479},
eprint = {2611.08479},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08479},
}
RIS
TY - UNPB
TI - Flat-band systems: A platform to realize the moments of Quantum Metric
AU - Rishi Gangadhar
AU - Binayyak Roy
AU - Vito Scarola
AU - Sumanta Tewari
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08479
UR - https://arxiv.org/abs/2611.08479
AB - The quantum metric is a fundamental geometric property of Bloch bands that governs a wide range of physical phenomena, yet experimentally accessing it remains challenging. We show that the momentum-space variation of the quantum metric can be probed through the real-space dynamics of a Gaussian wave packet prepared in an isolated flat band. Following the application of a weak constant force, we demonstrate analytically that the leading order change in the wave-packet variance is linear in time and contains a contribution proportional to the wave-packet averaged gradient of the quantum-metric trace. This geometric contribution remains finite despite the absence of band dispersion. We illustrate the effect using a gapped Lieb lattice with an exactly flat middle band and vanishing Berry curvature, allowing the quantum-metric contribution to the spreading to be isolated. The numerical results agree with the analytical prediction and confirm the quantum-metric contribution to the wave-packet spreading. The required lattice preparation, tunable hopping amplitudes, applied force, and density measurements are compatible with established ultracold-atom techniques, providing a possible platform for observing the predicted response. Our results establish wave-packet spreading as a dynamical probe of quantum geometry in flat-band systems.
ER -