Quantum scars and short-time survival probability in the PXP model

We characterize decay rate of survival probability, which is defined as the squared overlap amplitude between initial and time-evolved quantum state, in the PXP model with open boundary conditions. We investigate the role of anomalously slow thermalizing quantum states, so called quantum scar states, in determining the system's survival probability. We construct a theoretical model by splitting the local density of states (LDOS) into a Gaussian thermal contribution and a modulated Dirac comb describing the quantum scar contribution, and analytically calculate the survival probability. We find an exponential decay rate of the survival probability that increases linearly with the chain length, but with a nonuniversal slope that depends on the presence of scars in the LDOS. This agrees with our numerical results obtained by the time-evolving block-decimation (TEBD) method which allows us to compute the survival probability for PXP chains of up to 1000 qubits. Our results indicate that it is the contribution of quantum scars that dominates the survival probability decay in the short-time dynamics of the system. This is a signature of quantum scars that is readily measurable in existing experimental systems such as Rydberg atom quantum simulators.