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arXiv:2105.00014 · SciPost Physics

Bloch oscillations and the lack of the decay of the false vacuum in a one-dimensional quantum spin chain

O Pomponio, Miklós Antal Werner, Gergely Zaránd, G. Takács

Published Feb 15, 2022• 0 citations
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Abstract

We consider the decay of the false vacuum, realised within a quantum quench into an anti-confining regime of the Ising spin chain with a magnetic field opposite to the initial magnetisation. Although the effective linear potential between the domain walls is repulsive, the time evolution of correlations still shows a suppression of the light cone and a reduction of vacuum decay {via suppression of the growth of nucleated bubbles. The suppression of the bubble growth is a lattice effect, and can be assigned to emergent Bloch oscillations.

DOI
10.21468/scipostphys.12.2.061

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We consider the decay of the false vacuum, realised within a quantum quench into an anti-confining regime of the Ising spin chain with a magnetic field opposite to the initial magnetisation. Although the effective linear potential between the domain walls is repulsive, the time evolution of correlations still shows a suppression of the light cone and a reduction of vacuum decay {via suppression of the growth of nucleated bubbles. The suppression of the bubble growth is a lattice effect, and can be assigned to emergent Bloch oscillations.
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.
We consider non-equilibrium dynamics after quantum quenches in the mixed-field three-state Potts quantum chain in the ferromagnetic regime. Compared to the analogous setting for the Ising spin chain, the Potts model has a much richer phenomenology, which originates partly from baryonic excitations in the spectrum and partly from the various possible relative alignments of the initial magnetisation and the longitudinal field. We obtain the excitation spectrum by combining semiclassical approximation and exact diagonalisation, and we use the results to explain the various dynamical behaviours we observe. Besides recovering dynamical confinement, as well as Wannier-Stark localisation due to Bloch oscillations similar to the Ising chain, a novel feature is the presence of baryonic excitations in the quench spectroscopy. In addition, when the initial magnetisation and the longitudinal field are misaligned, both confinement and Bloch oscillations only result in partial localisation, with some correlations retaining an unsuppressed light-cone behaviour together with a corresponding growth of entanglement entropy.
We consider non-equilibrium dynamics after quantum quenches in the mixed-field three-state Potts quantum chain in the ferromagnetic regime. Compared to the analogous setting for the Ising spin chain, the Potts model has a much richer phenomenology, which originates partly from baryonic excitations in the spectrum and partly from the various possible relative alignments of the initial magnetisation and the longitudinal field. We obtain the excitation spectrum by combining semi-classical approximation and exact diagonalisation, and we use the results to explain the various dynamical behaviours we observe. Besides recovering dynamical confinement, as well as Wannier-Stark localisation due to Bloch oscillations similar to the Ising chain, a novel feature is the presence of baryonic excitations in the quench spectroscopy. In addition, when the initial magnetisation and the longitudinal field are misaligned, both confinement and Bloch oscillations only result in partial localisation, with some correlations retaining an unsuppressed light-cone behaviour together with a corresponding growth of entanglement entropy.
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.
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).