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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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Hydrodynamic transport and violation of the viscosity-to-entropy ratio bound in nodal-line semimetals
The ratio between the shear viscosity and the entropy η/s is considered a universal measure of the strength of interactions in quantum systems. This quantity was conjectured to have a universal lower bound (1/4π)h ̄/kB, which indicates a very strongly correlated quantum fluid. By solving the quantum kinetic theory for a nodal-line semimetal in the hydrodynamic regime, we show that η/s ∝ T violates the universal lower bound, scaling toward zero with decreasing temperature T in the perturbative limit. We find that the hydrodynamic scattering time between collisions is nearly temperature independent, up to logarithmic scaling corrections, and can be extremely short for large nodal lines, near the Mott-Ragel-Ioffe limit. Our finding suggests that nodal-line semimetals can be very strongly correlated quantum systems.
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- Award ID(s):
- 2024864
- PAR ID:
- 10294957
- Date Published:
- Journal Name:
- Physical review research
- Volume:
- 3
- ISSN:
- 2643-1564
- Page Range / eLocation ID:
- 033003
- 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/101103/PhysRevResearch.3.033003
