arXiv:1807.02108

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• Link
• Title: Signatures of integrability in the dynamics of Rydberg-blockaded chains
• Authors (optional): Vedika Khemani, Chris R. Laumann, and Anushya Chandran
• Reason (optional): Understanding PXP model and quantum scars from integrable approaching perspective.
• Keywords: Quantum Many-body scars

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Summary

• Main Proposal: Thermal behavior of PXP model might be controlled by an integrable parent model which has remaining effects as scars in experimental accessible region.
• “scar states” are the finite-size shadow of low entropy conserved sectors of the parent model.
• interesting observables: scaling of fluctuation across different energy against Hilbert space dimension

Problems

• Is integrable model gives $$r=0.39$$? How to remove degeneracies?

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Other proposals on slow dynamics in Rydberg atom experiments (quantum scars)

• Weak ergodicity breaking from quantum many-body scars, C. J. Turner , A. A. Michailidis, D. A. Abanin, M. Serbyn and Z. Papić , Nat. Phys. 14, 745.

  The enhancement of the participation ratio for special eigenstates evidences their concentration in some subregions of the Hilbert space. This suggests that special eigenstates are equivalent to the many-body version of quantum scarred wavefunctions that concentrate in the vicinity of unstable periodic classical orbits in the single-particle quantum chaos.

The quantum scar notations comes from the ipr calculation on many-body wavefunctions.

Results on Level statistics of PXP model:

There is a pronounced level repulsion. This is in sharp contrast with integrable systems, which always have Poisson level statistics.

The authors argued that the relevant model is far way from some integrable limit.

The Wigner–Dyson level statistics, along with ballistic growth of entanglement, rule out the integrability-based explanation of the non-ergodic dynamics in the model.

original experiment

• Bernien, H. et al. Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579–584 (2017). observation: Z2 configuration initial states have very slow dynamics.