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Coexistence of Different Scaling Laws for the Entanglement Entropy in a Periodically Driven System^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Results

## 3. Discussion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**(

**left**) For a non-critical (critical) system at $t=0$ an area (log) law for the entanglement entropy is satisfied. At $t>0$, the periodic drive is responsible for the appearence of quasi-particle travelling along the chain entangling the spins in the region they have spanned, i.e., $l=2{v}_{max}t$, and represented in the left figure by arrows. If the subsystem is chosen such that the arrows span over its whole size, every spin in it is entangled with spins outside and a volume law follows (blue box), otherwise an area (log) law holds (red box). A snapshot of the entanglement entropy for different subsystem sizes l in a spin chain of $N=8192$ for a periodic drive far from criticality after $n=480$ cycles (

**left**) and at criticality after $n=120$ cycles (

**right**). The insets show the coexistence of a volume with an area and with a log law, respectively.

**Figure 2.**(

**left**) Logarithmic divergence with the system size N of the half-chain entanglement entropy after $n=15$ cycles of the drive $h\left(t\right)=1+\frac{1}{2}sin\left(\right)open="("\; close=")">\pi t$. (

**right**) Finite-size scaling with the critical exponent $\nu =1$ of the Ising universality class of the data on the left panel close to $h={h}_{c}$.

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**MDPI and ACS Style**

Apollaro, T.J.G.; Lorenzo, S.
Coexistence of Different Scaling Laws for the Entanglement Entropy in a Periodically Driven System. *Proceedings* **2019**, *12*, 6.
https://doi.org/10.3390/proceedings2019012006

**AMA Style**

Apollaro TJG, Lorenzo S.
Coexistence of Different Scaling Laws for the Entanglement Entropy in a Periodically Driven System. *Proceedings*. 2019; 12(1):6.
https://doi.org/10.3390/proceedings2019012006

**Chicago/Turabian Style**

Apollaro, Tony J. G., and Salvatore Lorenzo.
2019. "Coexistence of Different Scaling Laws for the Entanglement Entropy in a Periodically Driven System" *Proceedings* 12, no. 1: 6.
https://doi.org/10.3390/proceedings2019012006