Bubble nucleation in long-range systems

About

Metastable states are ubiquitous in systems undergoing first-order transitions, where the decay proceeds via the nucleation of critical droplets. This phenomenon has attracted renewed interest driven by experiments with analog quantum simulators, which enable direct access to real-time nucleation dynamics.

Many of these platforms, trapped-ion Ising simulators, Rydberg-atom arrays with dipolar or van der Waals tails, exhibit long-range power-law couplings. Understanding how such interactions reshape the nucleation process is an open challenge. To address it, we introduce a numerical method based on solving the fractional-Laplacian saddle-point equation for the nucleating droplet, applicable to both thermal and quantum decay regimes. After benchmarking against the local case, we turn to the weak long-range setting.

We find that the critical droplet profile develops distinctive algebraic tails, in stark contrast to the sharp domain walls of short-range models. In the classical regime, we observe a metastability transition as a function of the interaction range: for sufficiently long-range couplings, the metastable state becomes arbitrarily long-lived as the energy splitting between the two phases vanishes, mirroring the equilibrium phase transition of the one-dimensional long-range Ising model. In the quantum (1+1)-dimensional case, the physics is qualitatively different: the interplay between long-range interactions and quantum fluctuations modifies the nucleation process in ways that have no classical analog, with distinct regimes emerging as the interaction range is varied.

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