Entanglement area law in interacting bosons from the Bose-Hubbard model to $\phi$4 theory and beyond

Abstract:The entanglement area law is a universal principle that characterizes quantum many-body phases and underpins tensor network algorithms. Traditionally, its validity has been limited to systems with short-range interactions and bounded local energy. Achieving a complete generalization that removes both of these constraints has been a longstanding goal in quantum many-body theory, especially for interacting boson systems where unbounded energy presents intrinsic difficulties. In this work, we rigorously prove the area law for one-dimensional interacting boson systems with long-range interactions, covering broad models including the Bose-Hubbard and $\phi4$ classes. Furthermore, we establish an efficiency guarantee for Matrix-Product-State approximations of the ground states, offering a practical route to numerical simulation. One of our main technical contributions is a general method for Hilbert space dimension reduction, whose applicability extends to arbitrary spatial dimensions. These results address two major challenges simultaneously and provide important foundations for simulating long-range cold atomic systems.

Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)

arXiv:2411.02157 [quant-ph]

(or arXiv:2411.02157v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2411.02157 Focus to learn more arXiv-issued DOI via DataCite

Nat. Commun. 17, 7294 (2026)

https://doi.org/10.1038/s41467-026-72404-w Focus to learn more DOI(s) linking to related resources

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.