Scaling of the entanglement spectrum in driving critical dynamics

TL;DR

This paper develops a scaling theory for the entanglement spectrum, specifically the Schmidt gap, under external driving, showing it signals critical points and estimates critical exponents across different scaling regions.

Contribution

The authors introduce a unified scaling theory for the entanglement spectrum's Schmidt gap under driving, bridging finite-size and finite-time scaling regimes.

Findings

Schmidt gap signals critical points in driven quantum systems.

The theory applies to both Ising and Potts models.

Schmidt gap estimates critical exponents accurately.

Abstract

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.