Statistical properties of the off-diagonal matrix elements of observables in eigenstates of integrable systems Article Swipe

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Observable Eigenvalues and eigenvectors Diagonal Boson Integrable system Diagonal matrix Matrix (chemical analysis) Dimension (graph theory) Physics Mathematical physics Quantum mechanics Statistical physics Mathematics Pure mathematics Geometry Materials science Composite material

Yicheng Zhang , Lev Vidmar , Marcos Rigol ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.1103/physreve.106.014132 · OA: W4221163161

We study the statistical properties of the off-diagonal matrix elements of observables in the energy eigenstates of integrable quantum systems. They have been found to be dense in the spin-1/2 XXZ chain, while they are sparse in noninteracting systems. We focus on the quasimomentum occupation of hard-core bosons in one dimension, and show that the distributions of the off-diagonal matrix elements are well described by generalized Gamma distributions, in both the presence and absence of translational invariance but not in the presence of localization. We also show that the results obtained for the off-diagonal matrix elements of observables in the spin-1/2 XXZ model are well described by a generalized Gamma distribution.