Related papers: Hilbert-space geometry of random-matrix eigenstates

Hilbert-space geometry of random-matrix eigenstates

URL: http://arxiv.org/abs/2011.03557v1
Date: Fri, 6 Nov 2020 19:00:07 GMT
Title: Hilbert-space geometry of random-matrix eigenstates
Authors: Alexander-Georg Penner, Felix von Oppen, Gergely Zarand, and Martin R. Zirnbauer
Abstract summary: We discuss the Hilbert-space geometry of eigenstates of parameter-dependent random-matrix ensembles. Our results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.
Score: 55.41644538483948
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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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