  We study the out-of-time-ordered correlator (OTOC) in a zero temperature two
dimensional conformal field theory (CFT) under evolution by a Liouvillian
composed of the Virasoro generators. A bound was conjectured in
arXiv:1812.08657 on the growth of the OTOC set by the Krylov complexity which
is a measure of operator growth. The latter grows as an exponential of time
with exponent $2\alpha$, which sets an upper bound on the Lyapunov exponent,
$\lambda_L \leq 2\alpha$. We find that for a two dimensional zero temperature
CFT, the OTOC decays exponentially with a Lyapunov exponent which saturates
this bound. We show that these Virasoro generators form the modular Hamiltonian
of the CFT with half space traced out. Therefore, evolution by this modular
Hamiltonian gives rise to thermal dynamics in a zero temperature CFT.
Leveraging the thermal dynamics of the system, we derive this bound in a zero
temperature CFT using the analyticity and boundedness properties of the OTOC.
