Entanglement Entropy of Disordered Quantum Wire Junctions

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.