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

TL;DR

This paper investigates real-time quantum false vacuum decay in a one-dimensional Ising model using matrix product states, revealing stages of bubble nucleation, growth, and lattice effects, with results matching analytical decay rates.

Contribution

It introduces a Gaussian ansatz for the quantum state evolution and demonstrates its effectiveness in describing bubble dynamics in lattice false vacuum decay.

Findings

Identification of three stages: nucleation, semi-classical growth, and Bloch oscillations.

Quantitative agreement of decay rate with analytical predictions.

Resonant bubbles are significant only in specific parameter regions.

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.