Quantum ergodicity in the SYK model

Bagrets, Dmitry
2018-05
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Quantum ergodicity in the SYK model

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2018-05

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In my talk I will discuss a replica path integral approach describing the quantum chaotic dynamics of the SYK model at large time scales [1]. The theory leads to the identification of non-ergodic collective modes which relax and eventually give way to an ergodic long time regime describable by random matrix theory (RMT). These modes, which play a role conceptually similar to the diffusion modes of dirty metals, carry quantum numbers which can be identified as the generators of the Clifford algebra: each of the 2^N different products that can be formed from N Majorana operators defines one effective mode. The competition between a decay rate quickly growing in the order of the product and a density of modes exponentially growing in the same parameter explains the characteristics of the system’s approach to the ergodic long time regime. I will present a number of analytical results for various spectral correlation functions which characterise the dynamics of the SYK model and demonstrate their favorable agreement with existing numerical data. [1] A. Altalnd and D. Bagrets, Nucl. Phys. B 930, 45-68 (2018)

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Bagrets, Dmitry. (2018). Quantum ergodicity in the SYK model. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/197507.

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