Krylov complexity in large q and double-scaled SYK model

• DOI: 10.1007/jhep08(2023)099
• Publication Date: 2023-08-18T07:02:49Z
• Authors: Budhaditya Bhatta...; Pratik Nandy; Tanay Pathak
• Keywords: Scrambling; Krylov subspace

A bstract Considering the large q expansion of Sachdev-Ye-Kitaev (SYK) model in two-stage limit, we compute Lanczos coefficients, Krylov complexity, and higher cumulants subleading order, along with t/q effects. The complexity naturally describes “size” distribution while encode richer information. We further consider double-scaled limit SYK at infinite temperature, where ~ $$ \sqrt{N} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>N</mml:mi> </mml:msqrt> </mml:math> . In such a find that scrambling time shrinks to zero, coefficients diverge. growth appears be “hyperfast”, which is previously conjectured associated de Sitter space.