Self-assembly Monte Carlo reveals localized entanglement in giant polymer melts

Topological entanglements are central to understanding and predicting the properties of polymer melts. Yet, they make equilibrium sampling computationally challenging, as decorrelation times grow rapidly with chain length. Here, we introduce a Monte Carlo scheme that bypasses typical computational bottlenecks by working in a self-assembly ensemble rather than at fixed composition. Strictly local moves efficiently propagate backbone reconnections across scales while conserving the number of linear chains, achieving near-linear scaling of decorrelation time with system size, ${\tau }_{\mathrm{e}\mathrm{q}}\sim V^{1.0}$. With this method, formulated for a fully-packed lattice, we equilibrate periodic systems totalling up to $\simeq 1.1\times {10}^9$ monomers, accessing a universal melt regime insensitive to lattice details. We analyze intra- and inter-chain entanglements for chains of up to $N\simeq 5\times {10}^5$ monomers, revealing that they manifest as localized knots and links rather than as global tangles. Finally, we show that the magnitude of the Gauss linking integral between neighbouring chains grows only as $N^{1\mathrm{/}4}$.