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

Sumilan Banerjee and Ehud Altman
Phys. Rev. B 95, 134302 – Published 19 April 2017
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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<pc(n) that depends on the fermion filling n. The scrambling dynamics throughout the non-Fermi-liquid (NFL) phase is characterized by a universal Lyapunov exponent λL2πT in the low-temperature limit; however, the temperature scale marking the crossover to the conformal regime vanishes continuously at the critical point pc. The residual entropy at T0, nonzero in the NFL, also vanishes continuously at the critical point. For p>pc the quadratic sites effectively screen the SYK dynamics, leading to a quadratic fixed point in the low-temperature and low-frequency limit. The interactions have a perturbative effect in this regime leading to scrambling with Lyapunov exponent λLT2.

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  • Received 7 November 2016

DOI:https://doi.org/10.1103/PhysRevB.95.134302

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsGravitation, Cosmology & AstrophysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Sumilan Banerjee1,2 and Ehud Altman1,3

  • 1Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
  • 2Department of Physics, Indian Institute of Science, Bangalore 560012, India
  • 3Department of Physics, University of California, Berkeley, California 94720, USA

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Issue

Vol. 95, Iss. 13 — 1 April 2017

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