  We study the time evolution of holographic mutual and tripartite information
for a zero temperature $CFT$, derives to a non-relativistic thermal Lifshitz
field theory by a quantum quench. We observe that the symmetry breaking does
not play any role in the phase space, phase of parameters of sub-systems, and
the length of disentangling transition. Nevertheless, mutual and tripartite
information indeed depend on the rate of symmetry breaking. We also find that
for large enough values of $\delta t$ the quantity $t_{eq}\delta t^{-1}$, where
$\delta t$ and $t_{eq}$ are injection time and equilibration time respectively,
behaves universally, $i.e.$ its value is independent of length of separation
between sub-systems. We also show that tripartite information is always
non-positive during the process indicates that mutual information is
monogamous.
