Size of bulk fermions in the SYK model

Lensky, Yuri D.; Qi, Xiao-Liang; Zhang, Pengfei

doi:10.1007/jhep10(2020)053

Size of bulk fermions in the SYK model

Journal Article · Thu Oct 08 00:00:00 EDT 2020 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep10(2020)053· OSTI ID:1853140

Lensky, Yuri D. ^[1]; Qi, Xiao-Liang ^[2]; Zhang, Pengfei ^[3]

Stanford Univ., CA (United States); Stanford Univ., CA (United States)
Stanford Univ., CA (United States)
California Institute of Technology (CalTech), Pasadena, CA (United States)

The study of quantum gravity in the form of the holographic duality has uncovered and motivated the detailed investigation of various diagnostics of quantum chaos. One such measure is the operator size distribution, which characterizes the size of the support region of an operator and its evolution under Heisenberg evolution. In this work, we examine the role of the operator size distribution in holographic duality for the Sachdev-Ye-Kitaev (SYK) model. Using an explicit construction of AdS₂ bulk fermion operators in a putative dual of the low temperature SYK model, we study the operator size distribution of the boundary and bulk fermions. Our result provides a direct derivation of the relationship between (effective) operator size of both the boundary and bulk fermions and bulk SL(2;$$\mathbb{R}$$) generators.

View Accepted Manuscript (DOE)

Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States); Stanford Univ., CA (United States); Univ. of California, Oakland, CA (United States)

Sponsoring Organization:: Hertz Foundation; National Science Foundation (NSF); USDOE Office of Science (SC), High Energy Physics (HEP); Walter Burke Institute for Theoretical Physics

Grant/Contract Number:: SC0019380

OSTI ID:: 1853140

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 10 Vol. 2020; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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Complexity growth of operators in the SYK model and in JT gravity Jian, Shao-Kai; Swingle, Brian; Xian, Zhuo-Yu Journal of High Energy Physics, Vol. 2021, Issue 3 https://doi.org/10.1007/jhep03(2021)014	journal	March 2021
Quantum operator growth bounds for kicked tops and semiclassical spin chains Yin, Chao; Lucas, Andrew Physical Review A, Vol. 103, Issue 4 https://doi.org/10.1103/physreva.103.042414	journal	April 2021

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