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Quantum Simulation

Hilbert-space geometry of random-matrix eigenstates

arXiv
Authors: Alexander-Georg Penner, Felix von Oppen, Gergely Zarand, Martin R. Zirnbauer

Year

2020

Paper ID

19502

Status

Preprint

Abstract Read

~2 min

Abstract Words

98

Citations

N/A

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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  • The geometry of multi-parameter families of quantum states is important in numerous contexts, including adiabatic or nonadiabatic quantum dynamics, quantum quenches, and the...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2011.03557 [2] arXiv https://arxiv.org/abs/2011.03557 [3] Publisher https://arxiv.org/abs/2011.03557

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