Entanglement Entropy of Disordered Quantum Wire Junctions

TL;DR

This study investigates how entanglement entropy scales in disordered quantum wire junctions, revealing universal behaviors in some models and junction-dependent variations in others, with implications for understanding quantum correlations in complex systems.

Contribution

It demonstrates the universal scaling of entanglement entropy in disordered junctions for certain models and explores how junction geometry affects entanglement in free-fermion systems.

Findings

Entanglement entropy scales logarithmically with arm length in studied models.

Universal effective central charge depends on the number of arms for RTIM and XX models.

Junction geometry influences entanglement behavior in free-fermion models.

Abstract

We consider different disordered lattice models composed of $M$ linear chains glued together in a star-like manner, and study the scaling of the entanglement between one arm and the rest of the system using a numerical strong-disorder renormalization group method. For all studied models, the random transverse-field Ising model (RTIM), the random XX spin model, and the free-fermion model with random nearest-neighbor hopping terms, the average entanglement entropy is found to increase with the length $L$ of the arms according to the form $S(L)=\frac{c_{\rm eff}}{6}\ln L+const$. For the RTIM and the XX model, the effective central charge $c_{\rm eff}$ is universal with respect to the details of junction, and only depends on the number $M$ of arms. Interestingly, for the RTIM $c_{\rm eff}$ decreases with $M$, whereas for the XX model it increases. For the free-fermion model, $c_{\rm eff}$ depends also on the details of the junction, which is related to the sublattice symmetry of the model. In this case, both increasing and decreasing tendency with $M$ can be realized with appropriate junction geometries.