Numerically Probing the Universal Operator Growth Hypothesis

Understand

Recently, a hypothesis on the complexity growth of unitarily evolving operators was presented.

• This hypothesis states that in generic, non-integrable many-body systems the so-called Lanczos coefficients associated with an autocorrelation function grow asymptotically linear, with a logarithmic correction in one-dimensional systems.
• In contrast, the growth is expected to be slower in integrable or free models.
• In the paper at hand, we numerically test this hypothesis for a variety of exemplary systems, including 1d and 2d Ising models as well as 1d Heisenberg models.