The Weyl-Heisenberg ensemble: hyperuniformity and higher Landau levels

Abstract

Weyl-Heisenberg ensembles are a class of determinantal point processes associated with the Schrödinger representation of the Heisenberg group. Hyperuniformity characterizes a state of matter for which (scaled) density fluctuations diminish towards zero at the largest length scales. We will prove that Weyl-Heisenberg ensembles are hyperuniform. Weyl-Heisenberg ensembles include as a special case a multi-layer extension of the Ginibre ensemble modeling the distribution of electrons in higher Landau levels, which has recently been object of study in the realm of the Ginibre-type ensembles associated with polyanalytic functions. In addition, the family of Weyl-Heisenberg ensembles includes new structurally anisotropic processes, where point-statistics depend on the different spatial directions, and thus provide a first means to study directional hyperuniformity.

17 pages, 2 figures. (Typos corrected.)

References in corpus (6)

• Room-Temperature Quantum Hall Effect in Graphene
• Hyperuniformity and its Generalizations
• Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory
• Statistical properties of determinantal point processes in high-dimensional Euclidean spaces
• Exactly Solvable Disordered Sphere-Packing Model in Arbitrary-Dimension Euclidean Spaces
• Discrete coherent states for higher Landau levels

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• Anomalous suppression of large-scale density fluctuations in classical and quantum spin liquids
• Two-Dimensional Elliptic Determinantal Point Processes and Related Systems
• Local number variances and hyperuniformity of the Heisenberg family of determinantal point processes
• Correlations in interacting electron liquids: Many-body statistics and hyperuniformity
• Entanglement entropy and hyperuniformity of Ginibre and Weyl-Heisenberg ensembles
• Quantum Phase Transitions in Long-Range Interacting Hyperuniform Spin Chains in a Transverse Field
• Mean and variance of the cardinality of particles in polyanalytic Ginibre processes via a quantization method
• On accumulated spectrograms for Gabor frames
• Theoretical Basis for Classifying Hyperuniform States of Two-Component Systems
• Empirical plunge profiles of time-frequency localization operators
• Precise Determination of the Long-Time Asymptotics of the Diffusion Spreadability of Two-Phase Media