TY - JOUR

T1 - Many-body quantum chaos and space-time translational invariance

AU - Chan, Amos

AU - Shivam, Saumya

AU - Huse, David A.

AU - De Luca, Andrea

N1 - Funding Information:
A.C. and A.D.L. warmly thank John Chalker for his guidance in related projects. D.A.H. thanks Grace Sommers and Michael Gullans for a related collaboration. D.A.H. is supported in part by NSF QLCI grant OMA-2120757. A.C. is supported by fellowships from the Croucher foundation and the PCTS at Princeton University. This publication is supported in part by the Princeton University Library Open Access Fund.
Publisher Copyright:
© 2022, The Author(s).

PY - 2022/12

Y1 - 2022/12

N2 - 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.

AB - 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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U2 - 10.1038/s41467-022-34318-1

DO - 10.1038/s41467-022-34318-1

M3 - Article

C2 - 36470877

AN - SCOPUS:85143337589

SN - 2041-1723

VL - 13

JO - Nature communications

JF - Nature communications

IS - 1

M1 - 7484

ER -