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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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Edge limits of truncated circular beta ensembles
We study the scaling limit of the rank-one truncation of various beta ensemble generalizations of classical unitary/orthogonal random matrices: the circular beta ensemble, the real orthogonal beta ensemble, and the circular Jacobi beta ensemble. We derive the scaling limit of the normalized characteristic polynomials and the point process limit of the eigenvalues near the point 1. We also treat multiplicative rank one perturbations of our models. Our approach relies on a representation of truncated beta ensembles given by Killip-Kozhan [24], together with the random operator framework developed in [42, 43, 44] to study scaling limits of beta ensembles.
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- Award ID(s):
- 2246435
- PAR ID:
- 10612855
- Publisher / Repository:
- Institute of Mathematical Statistics and Bernoulli Society
- Date Published:
- Journal Name:
- Electronic Journal of Probability
- Volume:
- 30
- ISSN:
- 1083-6489
- Page Range / eLocation ID:
- 1-46
- Subject(s) / Keyword(s):
- beta ensemble non-normal perturbation random differential operator random matrix
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1214/25-EJP1270
