A physical system is said to satisfy a thermal area law if the mutual
    information between two adjacent regions in the Gibbs state is controlled by
    the area of their boundary. Thermal area laws have been derived for systems
    with bounded local interactions such as quantum spin systems. However, for
    lattice bosons these arguments break down because the interactions are
    unbounded. We rigorously derive a thermal area law for a class of bosonic
    Hamiltonians in any dimension which includes the paradigmatic Bose-Hubbard
    model. The main idea to go beyond bounded interactions is to introduce a
    quasi-free reference state with artificially decreased chemical potential by
    means of a double Peierls-Bogoliubov estimate.

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