#
Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Model and Method

## 3. Entanglement Entropy

## 4. Phase Diagram from Entanglement

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**von Neumann entanglement entropy (disorder-averaged over ${10}^{4}$ samples when $W>0$) as a function of the total system size L for ${L}_{A}/L=1/2$, $\mu =0$, and periodic boundary conditions: (

**a**) In the clean case ($W=0$) for different values of $\Delta /t$; (

**b**) For $\Delta =0$ and different disorder strengths $W/t$. For $W=\Delta =0$, a fit to the expected logarithmic critical behavior, Equation (5), is plotted in black.

**Figure 2.**von Neumann entanglement entropy (disorder-averaged over ${10}^{4}$ samples when $W>0$) as a function of the total system size L for ${L}_{A}/L=1/2$, $\Delta /t=0.6$, and periodic boundary conditions, for different values of the disorder strength $W/t$. Different panels correspond to different chemical potential: (

**a**) $\mu /t=0$; (

**b**) $\mu /t=2$; (

**c**) $\mu /t=2.2$; (

**d**) $\mu /t=2.5$. Black and blue curves indicate fits to a logarithmic critical behavior, as in Equation (5).

**Figure 3.**(

**a**) The median (taken over ${10}^{4}$ realizations) of the gap ${\delta}_{A}$ between the first two eigenvalues of the single-particle entanglement spectrum [spectrum of the entanglement Hamiltonian, Equation (3)], as a function of the disorder $W/t$ for ${L}_{A}/L=1/2$, $\Delta /t=0.6$, $\mu =0$, and periodic boundary conditions, for different values of the total system size L. (

**b**) The constant coefficient ${\delta}_{\infty}$ in fitting the L dependence of ${\delta}_{A}$ to Equation (9) as a function of the disorder strength $W/t$. The inset shows a blow-up of the region where ${\delta}_{\infty}$ switches from zero to nonzero. Our method of determining the critical disorder strength ${W}_{c}$ is also indicated—see the text for further details.

**Figure 4.**Phase diagram as a function of the disorder strength $W/t$ and the chemical potential $\mu /t$ for three values of $\Delta $: (

**a**) $\Delta /t=0.3$, (

**b**) $\Delta /t=0.6$, (

**c**) $\Delta /t=1$. The hatched region is the topological superconductor phase, the other region is topologically trivial.

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**MDPI and ACS Style**

Levy, L.; Goldstein, M.
Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain. *Universe* **2019**, *5*, 33.
https://doi.org/10.3390/universe5010033

**AMA Style**

Levy L, Goldstein M.
Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain. *Universe*. 2019; 5(1):33.
https://doi.org/10.3390/universe5010033

**Chicago/Turabian Style**

Levy, Liron, and Moshe Goldstein.
2019. "Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain" *Universe* 5, no. 1: 33.
https://doi.org/10.3390/universe5010033