Abstract：

The entanglement area law is a fundamental principle that shapes the informational structure of quantum many-body systems and is critical for algorithms based on tensor networks. Traditionally, this law has been established under two key assumptions: the system must have bounded local energy and exhibit short-range interactions. However, extending the area law to scenarios with unbounded local energy and long-range interactions remains a significant challenge, particularly in bosonic systems where these standard assumptions do not hold. In this work, we affirm the validity of the entanglement area law across a broad class of one-dimensional interacting bosonic systems, including models such as the Bose-Hubbard and φ^4 models, as well as systems with long-range interactions. Our approach overcomes the limitations of conventional assumptions by showing subexponential decay in the boson number distribution due to repulsive interactions. Consequently, we establish that it is possible to approximate ground states using Matrix Product States (MPS) with quasipolynomial bond dimensions. These findings provide crucial insights for simulating bosonic systems with long-range interactions and advancing quantum simulation methodologies.