2018/12/31 by Daniel E. Parker, Xiangyu Cao, Alexander Avdoshkin +2 · 4 citations
Physics and Astronomy · #cond-mat.stat-mech #cond-mat.str-el #hep-th #nlin.CD #quant-ph
paper · pdf · doi:10.1103/physrevx.9.041017
published as Phys. Rev. X 9, 041017 (2019) · 18+9 pages, 10 figures, 1 table; accepted version
arxiv created 2019/10/24 · arxiv updated 2019/10/25
We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued fraction expansion of the Green's functions grow linearly with rate α in generic systems, with an extra logarithmic correction in 1d. The rate α --- an experimental observable --- governs the exponential growth of operator complexity in a sense we make precise. This exponential growth even prevails beyond semiclassical or large-N limits. Moreover, α upper bounds a large class of operator complexity measures, including the out-of-time-order correlator. As a result, we obtain a sharp bound on Lyapunov exponents λL ≤ 2 α, which complements and improves the known universal low-temperature bound λL ≤ 2 πT. We illustrate our results in paradigmatic examples such as non-integrable spin chains, the Sachdev-Ye-Kitaev model, and classical models. Finally we use the hypothesis in conjunction with the recursion method to develop a technique for computing diffusion constants.