The prevailing view on long-range correlations is that they typically attenuate uniformly with distance and temperature, as most interactions either exhibit short-range dominance or decay following a power law. In contrast to this belief, this Letter demonstrates that the intricate interplay between quasiperiodicity and the quasi-one-dimensional (1D) nature of subbands can result in strong long-range coupling without attenuation, a phenomenon referred to as an immortal interaction. Exemplifying a periodically stacked Fibonacci chain, we uncover an immortal interaction with greatly enhanced, persistent long-range coupling. Using negativity, it is shown that this interaction creates stable entanglement that endures over long distances and remains robust at finite temperatures. Additionally, unconventional logarithmic scaling entanglement is revealed, deviating from the traditional area law. These findings offer quasiperiodic quasi-1D systems as a prospective platform for sustaining stable entanglement across exceptionally long distances, even in the presence of finite-temperature effects.

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• Long-range interactions
• Quantum entanglement