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

Understand

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.