Time evolution of spread complexity in quenched Lipkin-Meshkov-Glick model

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.