Scaling of the entanglement spectrum in driving critical dynamics

We present a scaling theory for the entanglement spectrum under an external driving. Based on the static scaling of the Schmidt gap and the theory of finite-time scaling, we show that the Schmidt gap can signal the critical point and be used to estimate the critical exponents no matter in the finite-size scaling region or in the finite-time scaling region. Crossover between the two regions is also demonstrated. We verify our theory using both the one-dimensional transverse-field Ising model and the one-dimensional quantum Potts model. Our results confirm that the Schmidt gap can be regarded as a supplement to the local order parameter.