Krylov complexity in the IP matrix model
The IP matrix model is a simple large $N$ quantum mechanical model made up of an adjoint harmonic oscillator plus a fundamental harmonic oscillator. It is a model introduced previously as a toy model of the gauge theory dual of an AdS black hole. In the large $N$ limit, one can solve the Schwinger-Dyson equation for the fundamental correlator, and at sufficiently high temperature, this model shows key signatures of thermalization and information loss; the correlator decay exponentially in time, and the spectral density becomes continuous and gapless. We study the Lanczos coefficients $b_n$ in this model and at sufficiently high temperature, it grows linearly in $n$ with logarithmic corrections, which is one of the fastest growth under certain conditions. As a result, the Krylov complexity grows exponentially in time as $\sim \exp\left({\cal{O}{\left(\sqrt{t}\right) }}\right)$. These results indicate that the IP model at sufficiently high temperature is chaotic.