Entanglement Islands in 1D and 2D Lattices with Defects

We investigate the spatial structure of quantum entanglement in one- and two-dimensional lattice systems containing structural defects, using the Time-Dependent Quantum Monte Carlo (TDQMC) method. By constructing reduced density matrices from ensembles of guide waves, we resolve spatial variations in both Coulomb-mediated entanglement and coherence without requiring full many-body wavefunctions. This approach reveals localized regions, entanglement islands, where quantum correlations are enhanced or suppressed due to the presence of vacancies or interaction inhomogeneities. In 1D systems, entanglement tends to concentrate near defects, while in 2D systems, we observe bridge-like and radially symmetric domains. Our results demonstrate that TDQMC offers a scalable and physically transparent framework for real-space quantum information analysis, with implications for information transfer in atomic-size structures, quantum materials, entanglement-based sensing, and coherent state engineering.