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Fluctuations in Various Regimes of Non-hermiticity and a Holographic Principle
Faculty of Mathematics, Carlos III University of Madrid, Avda. de la Universidad, 30, 28911, Leganés, Spain.ORCID iD: 0000-0003-3760-111X
Faculty of Physics, Bielefeld University, P.O. Box 100131, 33501, Bielefeld, Germany.ORCID iD: 0000-0002-1710-4258
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Probability, Mathematical Physics and Statistics.ORCID iD: 0000-0002-7598-4521
2026 (English)In: Annales de l'Institute Henri Poincare. Physique theorique, ISSN 1424-0637, E-ISSN 1424-0661Article in journal (Refereed) Epub ahead of print
Abstract [en]

The variance of the number of particles in a set is an important quantity in understanding the statistics of non-interacting fermionic systems in low dimensions. An exact map of their ground state in a harmonic trap in one and two dimensions to the classical Gaussian unitary and complex Ginibre ensemble, respectively, allows to determine the counting statistics at finite and infinite system size. We will establish two new results in this setup. First, we uncover an interpolating central limit theorem between known results in one and two dimensions, for linear statistics of the elliptic Ginibre ensemble. We find an entire range of interpolating weak non-Hermiticity limits, given by a two-parameter family for the mesoscopic scaling regime. Second, we considerably generalize the proportionality between the number variance and the entanglement entropy between Fermions in a set A and its complement in two dimensions. Previously known only for rotationally invariant sets and external potentials, we prove a holographic principle for general non-rotationally invariant sets and random normal matrices. It states that both number variance and entanglement entropy are proportional to the circumference of A.

Place, publisher, year, edition, pages
Springer Nature , 2026.
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Condensed Matter Physics Algebra and Logic Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-383464DOI: 10.1007/s00023-026-01704-0ISI: 001779554500001Scopus ID: 2-s2.0-105040591180OAI: oai:DiVA.org:kth-383464DiVA, id: diva2:2072191
Note

QC 20260615

Available from: 2026-06-15 Created: 2026-06-15 Last updated: 2026-06-15Bibliographically approved

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Molag, L. D.Akemann, G.Duits, Maurice
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Probability, Mathematical Physics and Statistics
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Condensed Matter PhysicsAlgebra and LogicMathematical Analysis

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