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記
日時：２０１８年１１月０２日（金）１４時３０分〜
場所：東京大学 生産技術研究所 千葉実験所 研究実験棟Ｉn210号室
道程：http://hatano-lab.iis.u-tokyo.ac.jp/access.html
講師：伊與田英輝さん（東大工）
演題：Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models
要旨：The Sachdev-Ye-Kitaev (SYK) model attracts attention in the context of information scrambling, which represents delocalization of quantum information and is quantified by the out-of-time-ordered correlators (OTOC). The SYK model contains N fermions with disordered and four-body interactions. Using the fact that the two-point and four-point functions can be calculated analytically in the limit of large-N and low-energy limit, it is shown that the SYK model exhibits the fastest scrambling and saturates “the chaotic bound”. The SYK model has been investigated also in condensed matter physics because of its relevance to non-Fermi liquid, quantum criticality, and the effect of disorder in strongly correlated systems.
Here, we introduce a variant of the SYK model, which we refer to as the Wishart SYK model. We investigate the Wishart SYK model for complex fermions and that for hard-core bosons. We show that the ground state of the Wishart SYK model is massively degenerate and the residual entropy is extensive, and that the Wishart SYK model for complex fermions is integrable. In addition, we numerically investigate the OTOC and level statistics of the SYK models. At late times, the OTOC of the fermionic Wishart SYK model exhibits large temporal fluctuations, in contrast with smooth scrambling in the original SYK model. We argue that the large temporal fluctuations of the OTOC are a consequence of a small effective dimension of the initial state. We also show that the level statistics of the fermionic Wishart SYK model is in agreement with the Poisson distribution, while the bosonic Wishart SYK model obeys the GUE or the GOE distribution.
参考文献
[1] E. Iyoda, H. Katsura, and T. Sagawa, Phys. Rev. D 98, 086020 (2018).
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李 宰河
〒277-8574 千葉県柏市柏の葉5-1-5
東京大学生産技術研究所
e-mail: lee@iis.u-tokyo.ac.jp
Tel: 04-7136-6977
Fax: 04-7136-6978
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