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Hilbert-space geometry of random-matrix eigenstates
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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.
Forward citations
Cited by 2 Pith papers
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The universality class of the first levels in low-dimensional gravity
Near-edge states in dense chaotic systems and in JT gravity have a universal, analytically computed fidelity susceptibility distribution that is heavy-tailed yet parametrically more rigid than bulk states.
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Geometry of quantum states and chaos-integrability transition
Ensemble-averaged quantum metric tensors of random matrix models show finite geodesic distance to the chaotic phase and a 1/r divergence of fidelity susceptibility near integrability.
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