  We use the spread complexity of a time evolved state after a sudden quantum
quench in the Lipkin-Meshkov-Glick (LMG) model prepared in the ground state as
a probe of quantum phase transition when the system is quenched towards the
critical point. By studying the growth of the effective number of elements of
the Krylov basis, those contribute to the spread complexity more than a
preassigned cut off, we show how the two phases of the LMG model can be
distinguished. We also explore the time evolution of spread entropy after both
non-critical and critical quenches. We show that the sum contributing to the
spread entropy converges slowly in the symmetric phase of the LMG model
compared to that of the broken phase, and for a critical quench, the spread
entropy diverges logarithmically at late times.

High Energy Physics - Theory;Statistical Mechanics;Strongly Correlated Electrons;Quantum Physics