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arXiv:2608.11339

Operational identifiability of false-vacuum decay rates in the quantum Ising chain

Boliang Yu, Ruixin Zhou, Hang Su

cond-mat.stat-mechquant-phSubmitted Aug 11, 2026• Announced Aug 13, 2026• 0 citations
v1 · Aug 11, 2026v2 · Aug 14, 2026v3 · Aug 24, 2026
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Abstract

Extracting a thermodynamic nucleation rate from finite-time quantum dynamics requires separating observable decay from estimator and finite-size validity. We develop a multilevel identification framework to real-time tensor-network simulations of false-vacuum decay in the one-dimensional quantum Ising chain. Across twelve parameter points with non-empty analysis intervals, the same coherent two-kink amplitudes semi-quantitatively predict both infinite-chain survival and magnetization dynamics: the survival coefficient has a median lattice-to-theory ratio of 0.902, while the magnetization-area slope ratios span 0.809--0.953. By contrast, the microscopic nearest-neighbour bond response is coherence dominated: vacuum--pair coherence contributes 60.0--81.5\% within the seven parameter points satisfying the matched-bond-dimension convergence criterion, while substantial late-window slope discrepancies remain that cannot be removed by a scalar normalization. The framework establishes reliable finite-time decay coefficients and identifies the additional finite-size and branch-validation requirements for a bulk thermodynamic rate interpretation. Within the two-kink model, a lattice-resolved WKB action reduces the median fixed-prefactor discrepancy with the coherent-bubble spectral calculation to 4.13\%. Quantitative cross-level consistency, observable-dependent reduced-model error, and a thermodynamic-rate interpretation that remains subject to finite-size validation can therefore coexist.

Comments
23 pagse, 6 figures

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Extracting a thermodynamic nucleation rate from finite-time quantum dynamics requires separating observable decay from estimator and finite-size validity. We develop a multilevel identification framework to real-time tensor-network simulations of false-vacuum decay in the one-dimensional quantum Ising chain. Across twelve parameter points with non-empty analysis intervals, the same coherent two-kink amplitudes semi-quantitatively predict both infinite-chain survival and magnetization dynamics: the survival coefficient has a median lattice-to-theory ratio of 0.902, while the magnetization-area slope ratios span 0.809--0.953. By contrast, the microscopic nearest-neighbour bond response is coherence dominated: vacuum--pair coherence contributes 60.0--81.5% within the seven parameter points satisfying the matched-bond-dimension convergence criterion, while substantial late-window slope discrepancies remain that cannot be removed by a scalar normalization. The framework establishes reliable finite-time decay coefficients and identifies the additional finite-size and branch-validation requirements for a bulk thermodynamic rate interpretation. Within the two-kink model, a lattice-resolved WKB action reduces the median fixed-prefactor discrepancy with the coherent-bubble spectral calculation to 4.13%. Quantitative cross-level consistency, observable-dependent reduced-model error, and a thermodynamic-rate interpretation that remains subject to finite-size validation can therefore coexist.
Recent real-time simulations of false-vacuum decay in the quantum Ising chain report decay-rate prefactors that disagree with each other and with field theory by factors up to three. We prepare the metastable state by a real-time ramp of the longitudinal field, measure the survival rate per site of an infinite matrix-product state, and compare it with the decay rate that Fonseca and Zamolodchikov obtained from the free energy of the Ising field theory continued to negative field. At two lattice spacings and scaling variables y = 2.2–2.8 the ratio is 1.008 with a standard deviation of 0.015 over 6 runs, with no adjustable parameter, once the first correction to the thin-wall formula is kept. The two-kink coefficient π∆E/18 used in recent comparisons is too large by π2/9, as anticipated by Fonseca and Zamolodchikov, and exponential fits to the order parameter return rates 147–390 times larger than the nucleation rate. The survival rate, or equivalently the growth rate of the bubble density, is the observable that quantum simulators should compare with theory.
False vacuum decay describes the relaxation of a metastable state through the nucleation and growth of bubbles of the stable phase. Despite describing a broad variety of phenomena across different fields, the quantum version of the nucleation theory has little experimental or numerical support. Testing its predictions is particularly important in two or more spatial dimensions, where bubble nucleation acquires its true geometrical nature. Here, we study false vacuum decay in the quantum Ising model in two dimensions. Through tree tensor network simulations we extract the decay rate, the effective interface tension and the critical bubble size. We compare them to new semi-classical field theory calculations, and find excellent agreement. These results provide numerical evidence that the critical-bubble picture survives in an interacting quantum spin system in 2+1 dimensions.
Microscopic Dynamics of False Vacuum Decay in the 2+12+12+1D Quantum Ising Model
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+12+12+1D quantum Ising model, where a longitudinal field is used to energetically separate the two Z2\mathbb{Z}_2Z2​ 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.
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.
In this work, we theoretically investigate the false vacuum decay process in a ferromagnetic quantum spin-1/2 chain. We develop a many-body theory describing the nucleation and the coherent dynamics of true-vacuum bubbles that is analytically tractable and agrees with numerical matrix product state calculations in all parameter regimes up to intermediate times. This theory allows us to identify different regimes in the parameter space and unravel the underlying physical mechanisms, thus offering conceptual insight into the microscopic quantum dynamics of metastable states. In particular, analogies and differences with the cosmological false vacuum decay picture are highlighted and characterized in terms of experimentally observable quantities.
The false vacuum decay has been a central theme in physics for half a century with applications to cosmology and to the theory of fundamental interactions. This fascinating phenomenon is even more intriguing when combined with the confinement of elementary particles. Due to the astronomical timescales involved, the research has so far focused on theoretical aspects of this decay. The purpose of this Letter is to show that the false vacuum decay is accessible to current optical experiments as quantum analog simulators of spin chains with confinement of the elementary excitations, which mimic the high energy phenomenology but in one spatial dimension. We study the nonequilibrium dynamics of the false vacuum in a quantum Ising chain and in an XXZ ladder. The false vacuum is the metastable state that arises in the ferromagnetic phase of the model when the symmetry is explicitly broken by a longitudinal field. This state decays through the formation of ``bubbles'' of true vacuum. Using infinite volume time evolving block decimation (iTEBD) simulations, we are able to study the real-time evolution in the thermodynamic limit and measure the decay rate of local observables. We find that the numerical results agree with the theoretical prediction that the decay rate is exponentially small in the inverse of the longitudinal field.