2026/06/30 by J. Sirker
Physics and Astronomy · #cond-mat.dis-nn #cond-mat.stat-mech #cond-mat.str-el
The path-entropy obstruction theorem concerning the perturbative construction of LIOMs has been rewritten and significantly sharpened. Also, parts of theorems 3 and 5 have been reformulated in more general terms, and no longer rely on the asymptotic operator growth formula
arxiv created 2026/08/05 · arxiv updated 2026/08/06
For the disordered Ising chain with transverse and longitudinal fields, where couplings and fields are drawn from strictly positive distributions, Cao~\citeCao has shown that the moments μ2k = ‖[H,σz0](k)‖22 grow almost factorially, μ2k1/(2k)∼ k/ln k, and thus asymptotically at the maximal allowed rate. We generalize this result by resolving the operator norm in support length and show that the weight at length ℓk ∼ k/ln k already exhibits almost factorial growth, ‖[H,σz0](k)ℓk‖2 \gtrsim (k/ln k)k. This implies maximal spatial delocalization of local operators and, in particular, rules out dynamical locality---the strongest form of many-body localization---at any disorder strength. We further establish rigorously a finite-size crossover scale L∼ (W/J)2, where W is the disorder and J the coupling strength. For L\lesssim (W/J)2 numerical studies only access a pre-asymptotic regime. Finally, we identify a structural path-entropy obstruction to perturbative LIOM constructions, based on the almost factorial branching of operator content and independent of resonance effects; the same mechanism strongly suggests ballistic real-time operator spreading, so sub-ballistic or localized dynamics would require a presently unidentified cancellation principle acting on almost factorially many disorder-dependent paths with random amplitudes.