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Conference on Quark Confinement and the Hadron Spectrum (Confinement)

Confinement and False Vacuum Decay in Quantum Spin Chains

Gianluca Lagnese

Published Oct 24, 2025• 0 citations
Publisher

Abstract

The confinement of elementary particles and the decay of the false vacuum are two paradigmatic predictions of quantum field theory. In their simplest formulation, the two phenomena can be understood as two facets of an underlying symmetry-breaking mechanism: the degeneracy of a double-degenerate vacuum is lifted by adding an explicit symmetry-breaking external field. Confined states are false vacuum bubbles within a true vacuum (the true ground state of the model); likewise, false vacuum decay refers to the dissolution of the metastable vacuum through true vacuum bubbles nucleation via quantum tunneling. The interest in this area of research has been recently revamped by the advances in experimental techniques (e.g. trapped ions, ultracold atoms, Rydberg atoms): confinement has already proved to be accessible in condensed matter laboratory experiments while the direct laboratory study of the false vacuum decay is promisingly within reach. Moreover, in the past few decades the out-of-equilibrium dynamics of quantum many-body systems was promoted to the forefront of research in condensed matter physics. I will present relevant investigations of such phenomena in the context of quantum spin chain models through the observation of their real-time dynamics following a quantum quench (the paradigmatic theoretical and experimental protocol for non-equilibrium dynamics).

DOI
10.22323/1.483.0182

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The confinement of elementary particles and the decay of the false vacuum are two paradigmatic predictions of quantum field theory. In their simplest formulation, the two phenomena can be understood as two facets of an underlying symmetry-breaking mechanism: the degeneracy of a double-degenerate vacuum is lifted by adding an explicit symmetry-breaking external field. Confined states are false vacuum bubbles within a true vacuum (the true ground state of the model); likewise, false vacuum decay refers to the dissolution of the metastable vacuum through true vacuum bubbles nucleation via quantum tunneling. The interest in this area of research has been recently revamped by the advances in experimental techniques (e.g. trapped ions, ultracold atoms, Rydberg atoms): confinement has already proved to be accessible in condensed matter laboratory experiments while the direct laboratory study of the false vacuum decay is promisingly within reach. Moreover, in the past few decades the out-of-equilibrium dynamics of quantum many-body systems was promoted to the forefront of research in condensed matter physics. I will present relevant investigations of such phenomena in the context of quantum spin chain models through the observation of their real-time dynamics following a quantum quench (the paradigmatic theoretical and experimental protocol for non-equilibrium dynamics).
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.
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.
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.
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.
Abstract The quantum decay of a relativistic scalar field from a metastable state (‘false vacuum decay’) is a fundamental idea in quantum field theory and cosmology. This occurs via local formation of bubbles of true vacuum with their subsequent rapid expansion. It can be considered as a relativistic analog of a first-order phase transition in condensed matter. Here we expand upon our recent proposal (Fialko O et al 2015 Europhys. Lett. 110 56001 ) for an experimental test of false vacuum decay using an ultra-cold spinor Bose gas. A false vacuum for the relative phase of two spin components, serving as the unstable scalar field, is generated by means of a modulated linear coupling of the spin components. We analyze the system theoretically using the functional integral approach and show that various microscopic degrees of freedom in the system, albeit leading to dissipation in the relative phase sector, will not hamper the observation of the false vacuum decay in the laboratory. This is well supported by numerical simulations demonstrating the spontaneous formation of true vacuum bubbles on millisecond time-scales in two-component 7 Li or 41 K bosonic condensates in one-dimensional traps of ∼ 100 μ m size.
In quantum field theory, the decay of an extended metastable state into the real ground state is known as ``false vacuum decay'' and it takes place via the nucleation of spatially localized bubbles. Despite the large theoretical effort to estimate the nucleation rate, experimental observations were still missing. Here, we observe bubble nucleation in isolated and highly controllable superfluid atomic systems, and we find good agreement between our results, numerical simulations and instanton theory opening the way to the emulation of out-of-equilibrium quantum field phenomena in atomic systems.