Many-body quantum chaos and space-time translational invariance

Chan, A. and Shivam, S. and Huse, D.A. and De Luca, A. (2022) Many-body quantum chaos and space-time translational invariance. Nature Communications, 13 (1). ISSN 2041-1723

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We study the consequences of having translational invariance in space and time in many-body quantum chaotic systems. We consider ensembles of random quantum circuits as minimal models of translational invariant many-body quantum chaotic systems. We evaluate the spectral form factor as a sum over many-body Feynman diagrams in the limit of large local Hilbert space dimension q. At sufficiently large t, diagrams corresponding to rigid translations dominate, reproducing the random matrix theory (RMT) behaviour. At finite t, we show that translational invariance introduces additional mechanisms via two novel Feynman diagrams which delay the emergence of RMT. Our analytics suggests the existence of exact scaling forms which describe the approach to RMT behavior in the scaling limit where both t and L are large while the ratio between L and LTh(t), the many-body Thouless length, is fixed. We numerically demonstrate, with simulations of two distinct circuit models, that the resulting scaling functions are universal in the scaling limit.

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Journal Article
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Nature Communications
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16 Dec 2022 12:20
Last Modified:
10 Jan 2023 17:55