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arXiv · 1610.04619

Solvable model for a dynamical quantum phase transition from fast to slow scrambling

Sumilan Banerjee·Ehud Altman
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Abstract

We propose an extension of the Sachdev-Ye-Kitaev (SYK) model that exhibits a quantum phase transition from the previously identified non-Fermi liquid fixed point to a Fermi liquid like state, while still allowing an exact solution in a suitable large $N$ limit. The extended model involves coupling the interacting $N$-site SYK model to a new set of $pN$ peripheral sites with only quadratic hopping terms between them. The conformal fixed point of the SYK model remains a stable low energy phase below a critical ratio of peripheral sites $p p_c$ the quadratic sites effectively screen the SYK dynamics, leading to a quadratic fixed point in the low temperature and frequency limit. The interactions have a perturbative effect in this regime leading to scrambling with Lyapunov exponent $λ_L\propto T^2$.

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Sumilan Banerjee, Ehud Altman. 2016-11-07. Solvable model for a dynamical quantum phase transition from fast to slow scrambling. https://doi.org/10.1103/physrevb.95.134302

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