Time Evolution of Entanglement Entropy in Quenched Holographic Superconductors

TL;DR

This paper studies how entanglement entropy evolves over time in a holographic superconductor model after a quench, revealing non-monotonic behavior, linear growth bounds, and a dynamical transition linked to the scalar order parameter.

Contribution

It provides a detailed analysis of the time evolution of entanglement entropy in quenched holographic superconductors, including bounds on growth velocity and transition points.

Findings

Entanglement entropy shows non-monotonic time dependence with a dip, linear growth, and saturation.

The linear growth velocity has an upper bound for large strip widths.

Late-time equilibrium entanglement entropy scales with quench strength following a power law.

Abstract

We investigate the dynamical evolution of entanglement entropy in a holographic superconductor model by quenching the source term of the dual charged scalar operator. By access to the full background geometry, the holographic entanglement entropy is calculated for a strip geometry at the AdS boundary. It is found that the entanglement entropy exhibits a robust non-monotonic behaviour in time, independent of the strength of Gaussian quench and the size of the strip: it first displays a small dip, then grows linearly, and finally saturates. In particular, the linear growth velocity of the entanglement entropy has an upper bound for strip with large width; The equilibrium value of the non-local probe at late time shows a power law scaling behaviour with respect to the quench strength; Moreover, the entanglement entropy can uncover the dynamical transition at certain critical quench strength which happens to coincide with the one obtained form the dynamical evolution of scalar order parameter.