Operator growth in Many Body Localized systems

There has been recent attention to the use of the Lanczos recursion method in characterizing chaotic systems. Operators evolve in time under the Louivillian superoperator. The recursion method builds a Krylov basis with repeated application of the Louivillian, and outputs a sequence of positive numbers called the “Lanczos coefficients” and an orthonormal basis for the Krylov space. In this basis, the Louivillian is tridiagonal with the Lanczos coefficients on the off-diagonals.

These coefficients parametrize the growth of complexity of the operator used to generate them. In this talk, I will analyze the behavior of these coefficients in large disordered XXZ spin chains, in regimes often characterized as many-body localized. I will look at their behavior both with and without an added thermal inclusion (region of much lower average disorder) and provide evidence for the absence of localization.