Universität zu Köln

Penner, Alexander-Georg ORCID: 0000-0003-2868-6553, von Oppen, Felix, Zarand, Gergely and Zirnbauer, Martin R. (2021). Hilbert Space Geometry of Random Matrix Eigenstates. Phys. Rev. Lett., 126 (20). COLLEGE PK: AMER PHYSICAL SOC. ISSN 1079-7114

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Abstract

The geometry of multiparameter 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Penner, Alexander-Georg UNSPECIFIED orcid.org/0000-0003-2868-6553 UNSPECIFIED von Oppen, Felix UNSPECIFIED UNSPECIFIED UNSPECIFIED Zarand, Gergely UNSPECIFIED UNSPECIFIED UNSPECIFIED Zirnbauer, Martin R. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-584926
DOI:	10.1103/PhysRevLett.126.200604
Journal or Publication Title:	Phys. Rev. Lett.
Volume:	126
Number:	20
Date:	2021
Publisher:	AMER PHYSICAL SOC
Place of Publication:	COLLEGE PK
ISSN:	1079-7114
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language CURVATURE DISTRIBUTION; EIGENVALUE CURVATURES; ENERGY-LEVELS; QUANTUM; SYMMETRY; SUPERBOSONIZATION; UNIVERSALITY; STATISTICS; PHYSICS Multiple languages Physics, Multidisciplinary Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/58492