2023/07/23 by Fabian H. L. Eßler, Essler, F. H. L., A. J. J. M. de Klerk +1 · 4 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2307.12410
openalex publication_date 2023/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the statistics of matrix elements of local operators in the basis of energy eigenstates in a paradigmatic integrable many-particle quantum theory, the Lieb-Liniger model of bosons with repulsive delta-function interaction. Using methods of quantum integrability we determine the scaling of matrix elements with system size. As a consequence of the extensive number of conservation laws the structure of matrix elements is fundamentally different from, and much more intricate than, the predictions of the eigenstate thermalization hypothesis for generic models. We uncover an interesting connection between this structure for local operators in interacting integrable models, and the one for local operators that are not local with respect to the elementary excitations in free theories. We find that typical off-diagonal matrix elements ⟨\boldsymbolμ|O|\boldsymbolλ⟩ in the same macro-state scale as exp(-c OLln(L)-LMO\boldsymbolμ,\boldsymbolλ) where the probability distribution function for MO\boldsymbolμ,\boldsymbolλ are well described by Fréchet distributions and cO depends only on macro-state information. In contrast, typical off-diagonal matrix elements between two different macro-states scale as exp(-d OL2), where dO depends only on macro-state information. Diagonal matrix elements depend only on macro-state information up to finite-size corrections.