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Abstract 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 L Th ( 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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This content will become publicly available on June 18, 2026
FeynHex User Guide
FeynHex is a free and open-source educational tool for building Feynman diagrams. We built this tool to provide an accurate representation of Feynman diagrams that can be physically explored by students. This a repository of the 3D models, documentation, and curriculum.
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- Award ID(s):
- 2209769
- PAR ID:
- 10621412
- Publisher / Repository:
- https://gitlab.com/feynhex
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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