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arXiv · 2011.03557

Hilbert-space geometry of random-matrix eigenstates

Alexander-Georg Penner·Felix von Oppen·Gergely Zarand·Martin R. Zirnbauer
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Abstract

The geometry of multi-parameter families of quantum states is important in numerous contexts, including adiabatic or nonadiabatic quantum dynamics, quantum quenches, and the characterization of quantum critical points. Here, we discuss the Hilbert-space geometry of eigenstates of parameter-dependent random-matrix ensembles, deriving the full probability distribution of the quantum geometric tensor for the Gaussian Unitary Ensemble. Our analytical results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We discuss relations to Levy stable distributions and compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.

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Alexander-Georg Penner, Felix von Oppen, Gergely Zarand, Martin R. Zirnbauer. 2020-11-06. Hilbert-space geometry of random-matrix eigenstates. https://doi.org/10.1103/physrevlett.126.200604

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