Scaling of Entanglement Entropy in the Random Singlet Phase

TL;DR

This paper provides numerical evidence that entanglement entropy in critical random spin chains scales logarithmically, confirming theoretical predictions and visually demonstrating the Random Singlet Phase through entanglement properties.

Contribution

It offers large-scale numerical validation of the logarithmic entanglement scaling in the Random Singlet Phase, aligning with recent theoretical predictions.

Findings

Logarithmic scaling of entanglement entropy confirmed

Numerical results match real-space RG predictions

First visual proof of the Random Singlet Phase via entanglement

Abstract

We present numerical evidences for the logarithmic scaling of the entanglement entropy in critical random spin chains. Very large scale exact diagonalizations performed at the critical XX point up to L=2000 spins 1/2 lead to a perfect agreement with recent real-space renormalization-group predictions of Refael and Moore [Phys. Rev. Lett. {\bf 93}, 260602 (2004)] for the logarithmic scaling of the entanglement entropy in the Random Singlet Phase with an effective central charge ${\tilde{c}}=c\times \ln 2$. Moreover we provide the first visual proof of the existence the Random Singlet Phase thanks to the quantum entanglement concept.