Microscopic Dynamics of False Vacuum Decay in the $2+1$D Quantum Ising Model

TL;DR

This paper investigates the microscopic dynamics of false vacuum decay in the 2+1D quantum Ising model using tensor network simulations, revealing how bubble fate depends on geometry and parameters, and proposing quantum simulation schemes.

Contribution

It introduces a detailed simulation of bubble nucleation and decay in the 2+1D quantum Ising model, linking microscopic features to the bubble's evolution and suggesting experimental quantum simulation methods.

Findings

Bubble fate depends on geometry and Hamiltonian parameters.

Simulations identify conditions for bubble expansion or collapse.

Proposes quantum simulation schemes for experimental probing.

Abstract

False vacuum decay, which is understood to happen through bubble nucleation, is a prominent phenomenon relevant to elementary particle physics and early-universe cosmology. Understanding its microscopic dynamics in higher spatial dimensions is currently a major challenge and research thrust. Recent advances in numerical techniques allow for the extraction of related signatures in tractable systems in two spatial dimensions over intermediate timescales. Here, we focus on the $2+1$D quantum Ising model, where a longitudinal field is used to energetically separate the two $\mathbb{Z}_2$ symmetry-broken ferromagnetic ground states, turning them into a ``true'' and ``false'' vacuum. Using tree tensor networks, we simulate the microscopic dynamics of a spin-down domain in a spin-up background after a homogeneous quench, with parameters chosen so that the domain corresponds to a bubble of the true vacuum in a false-vacuum background. Our study identifies how the ultimate fate of the bubble -- indefinite expansion or collapse -- depends on its geometrical features and on the microscopic parameters of the Ising Hamiltonian. We further provide a realistic quantum-simulation scheme, aimed at probing bubble dynamics on atomic Rydberg arrays.