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arXiv · 2508.13645

Real-time bubble nucleation and growth for false vacuum decay on the lattice

Daan Maertens·Jutho Haegeman·Karel Van Acoleyen
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Abstract

We revisit quantum false vacuum decay for the one-dimensional Ising model, focusing on the real-time nucleation and growth of true vacuum bubbles. Via matrix product state simulations, we demonstrate that for a wide range of parameters, the full time-dependent quantum state is well described by a Gaussian ansatz in terms of domain wall operators, with the associated vacuum bubble wave function evolving according to the linearized time-dependent variational principle. The emerging picture shows three different stages of evolution: an initial nucleation of small bubbles, followed by semi-classical bubble growth, which in turn is halted by the lattice phenomenon of Bloch oscillations. Furthermore, we find that the resonant bubble only plays a significant role in a certain region of parameter-space. However, when significant, it does lead to an approximately constant decay rate during the intermediate stage. Moreover, this rate is in quantitative agreement with the analytical result of Rutkevich (Phys. Rev. B 60, 14525) for which we provide an independent derivation based on the Gaussian ansatz.

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Daan Maertens, Jutho Haegeman, Karel Van Acoleyen. 2025-08-19. Real-time bubble nucleation and growth for false vacuum decay on the lattice. https://arxiv.org/abs/2508.13645

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