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

arXiv:2411.02157 · quant-ph, cond-mat.quant-gas, cond-mat.stat-mech, math-ph, math.MP · Submitted 2024-11-04 · Read on arXiv

quant-ph, cond-mat.quant-gas, cond-mat.stat-mech, math-ph, math.MP

Submitted: 2024-11-04

Updated: 2026-09-24

Comments: 14 pages, 4 figures; 79 pages Supplementary Material

Journal ref: Nat. Commun. 17, 7294 (2026)

DOI: 10.1038/s41467-026-72404-w

License: http://creativecommons.org/licenses/by/4.0/

The gist: The entanglement area law is a universal principle that characterizes quantum many-body phases and underpins tensor network algorithms.

Terminology

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.

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