Universal correlations in chaotic many-body quantum states: Fock-space formulation of Berrys random wave model (2403.10132v2)
Abstract: The apparent randomness of chaotic eigenstates in interacting quantum systems hides subtle correlations dynamically imposed by their finite energy per particle. These correlations are revealed when Berrys approach for chaotic eigenfunctions in single-particle systems is lifted into many-body space. We achieve this by a many-body semiclassics analysis, appropriate for the mesoscopic regime of large but finite number of particles. We then identify the universality of both the cross-correlations and the Gaussian distribution of expansion coefficients as the signatures of chaotic eigenstates. Combined, these two aspects imprint a distinctive backbone to the morphology of eigenstates that we check against extensive quantum simulations. The universality of eigenstate correlations for fixed energy density is then a further signature of many-body quantum chaos that, while consistent with the eigenstate thermalization hypothesis, lies beyond random matrix theory.
- Note1, following standard terminology we use ”single particle” instead of the more precise ”first-quantized” nomenclature for systems where the classical limit corresponds to particle-like (instead of field-like) degrees of freedom
- Note3, we assume η𝜂\etaitalic_η to be large compared to the local mean level spacing which implies a large number of eigenstates inside the spectral window.
- A. Voros, Annales de l’Institut Henri Poincaré 24 (1976)
- Note6, similar results are obtained for any seed state under the conditions discussed below
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