Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective Article Swipe

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YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2507.23028

The quantum geometric tensor and quantum Fisher information have recently been shown to provide a unified geometric description of the linear response of many-body systems. However, a similar geometric description of higher-order perturbative phenomena including nonlinear response in generic quantum systems is lacking. In this work, we develop a general framework for the time-dependent quantum geometry of many-body systems by treating external perturbing fields as coordinates on the space of density matrices. We use the Bures distance between the initial and time-evolved density matrix to define geometric quantities through a perturbative expansion. To lowest order, we derive a time-dependent generalization of the Bures metric related to the spectral density of linear response functions, unifying previous results for the quantum metric in various limits and providing a geometric interpretation of Fermi's golden rule. At next order in the expansion, we define a time-dependent Bures-Levi-Civita connection for general many-body systems. We show that the connection is the sum of one contribution that is related to a second-order nonlinear response function, and a second contribution that captures the higher geometric structure of first-order perturbation theory. We show that in the quasistatic, zero-temperature limit for noninteracting fermions, this Bures connection reduces to the known expression for band-theoretic Christoffel symbols. Our work provides a systematic framework to explore many-body quantum geometry beyond the quantum metric and highlights how higher-order correlation functions can probe this geometry.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2507.23028
PDF: https://arxiv.org/pdf/2507.23028
OA Status: green
OpenAlex ID: https://openalex.org/W4414931045

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DOI: https://doi.org/10.48550/arxiv.2507.23028

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Title: Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective

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Type: preprint

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Language: en

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Publication year: 2025

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Publication date: 2025-07-30

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Authors: Yafu Guan, Barry Bradlyn

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Landing page: https://arxiv.org/abs/2507.23028

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PDF URL: https://arxiv.org/pdf/2507.23028

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Cited by: 0

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