2020/12/31 by Xiangyu Cao · 1 citation
Physics and Astronomy · #cond-mat.stat-mech #hep-th #quant-ph
paper · pdf · doi:10.1088/1751-8121/abe77c
published as J. Phys. A: Math. Theor. 54 144001 (2021) · 9 pages, 0 figures; v2: accepted version, minor revisions
arxiv created 2021/06/10 · arxiv updated 2021/06/11
It was recently conjectured that in generic quantum many-body systems, the spectral density of local operators has the slowest high-frequency decay as permitted by locality. We show that the infinite-temperature version of this "universal operator growth hypothesis" holds for the quantum Ising spin model in d ≥ 2 dimensions, and for the chaotic Ising chain (with longitudinal and transverse fields) in one dimension. Moreover, the disordered chaotic Ising chain that exhibits many-body localization can have the same high-frequency spectral density decay as thermalizing models. Our argument is statistical in nature, and is based on the observation that the moments of the spectral density can be written as a sign-problem-free sum over paths of Pauli string operators.