Theory Seminar: Quantum chaos in the Brownian SYK model with large finite N: OTOCs and tripartite information

Christoph Sünderhauf (MPQ Theory Department)
The Brownian SYK model features all-to-all interactions of Majorana fermions with time-dependent disordered couplings.

September 04, 2019

Christoph Sünderhauf (MPQ Theory Department)
Herbert-Walther Lecture Hall G0.25
Wed, 4. September 2019, 11:30 am

Abstract:

The Brownian SYK model features all-to-all interactions of Majorana fermions with time-dependent disordered couplings. Quantum chaos and scrambling can be diagnosed with out-of-time ordered correlators (OTOCs) and the tripartite information. After introducing these concepts, I will focus on their computation in the Brownian SYK model. Exploiting permutational symmetry of averaged quantities leads to a description as an imaginary-time quench problem in terms of bosonic collective modes. Thus, we devise a method to calculate the diagnostics of scrambling within an effective Hilbert space growing merely linearly or quadratically with N. Since this enables us to study large systems up to a million particles numerically exactly, we can explicitly uncover a scrambling time logarithmic in N. Further, we demonstrate the decay to Haar-scrambling values at late times.

The talk is based on our recent work arXiv:1908.00775.

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