Length-resolved Operator Growth and Path-Entropy Obstructions to Many-Body Localization (opens in new tab)

For the disordered Ising chain with transverse and longitudinal fields, where couplings and fields are drawn from strictly positive distributions, Cao~\cite{Cao} has shown that the moments $\mu_{2k} = \|[H,\sigma^z_0]^{(k)}\|_2^2$ grow almost factorially, $\mu_{2k}^{1/(2k)}\sim k/\ln k$, 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 leng...