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Register a new userBloch oscillations and the lack of the decay of the false vacuum in a one-dimensional quantum spin chain
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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. The suppressed decay is a lattice effect, and can be assigned to emergent Bloch oscillations.
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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 time scales 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 non-equilibrium 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 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.
We study a false vacuum decay in a two-dimensional black hole spacetime background. The decay rate in the case that nucleation site locates at a black hole center has been calculated in the literature. We develop a method for calculating the decay rate of the false vacuum for a generic nucleation site. We find that the decay rate becomes larger when the nucleation site is close to the black hole horizon and coincides with that in Minkowski spacetime when the nucleation site goes to infinity.
We study the real-time dynamics of a small bubble of false vacuum in a quantum spin chain near criticality, where the low-energy physics is described by a relativistic (1+1)-dimensional quantum field theory. Such a bubble can be thought of as a confined kink-antikink pair (a meson). We carefully construct bubbles so that particle production does not occur until the walls collide. To achieve this in the presence of strong correlations, we extend a Matrix Product State (MPS) ansatz for quasiparticle wavepackets [Van Damme et al., arXiv:1907.02474 (2019)] to the case of confined, topological quasiparticles. By choosing the wavepacket width and the bubble size appropriately, we avoid strong lattice effects and observe relativistic kink-antikink collisions. We use the MPS quasiparticle ansatz to detect scattering outcomes: In the Ising model, with transverse and longitudinal fields, we do not observe particle production despite nonintegrability (supporting recent observations of nonthermalizing mesonic states). With additional interactions, we see production of confined and unconfined particle pairs. Although we simulated these low-energy, few-particle events with moderate resources, we observe significant growth of entanglement with energy and with the number of collisions, suggesting that increasing either will ultimately exhaust our methods. Quantum devices, in contrast, are not limited by entanglement production, and promise to allow us to go far beyond classical methods. We anticipate that kink-antikink scattering in 1+1 dimensions will be an instructive benchmark problem for relatively near-term quantum devices.
The decay rate of a false vacuum is studied in gauge theory, paying particular attention to its gauge invariance. Although the decay rate should not depend on the gauge parameter $xi$ according to the Nielsen identity, the gauge invariance of the result of a perturbative calculation has not been clearly shown. We give a prescription to perform a one-loop calculation of the decay rate, with which a manifestly gauge-invariant expression of the decay rate is obtained. We also discuss the renormalization necessary to make the result finite, and show that the decay rate is independent of the gauge parameter even after the renormalization.
Under a perfect periodic potential, the electric current density induced by a constant electric field may exhibit nontrivial oscillations, so-called Bloch oscillations, with an amplitude that remains nonzero in the large system size limit. Such oscillations have been well studied for nearly noninteracting particles and observed in experiments. In this work, we revisit Bloch oscillations in strongly interacting systems. By analyzing the spin-1/2 XXZ chain, which can be mapped to a model of spinless electrons, we demonstrate that the current density at special values of the anisotropy parameter $Delta=-cos(pi/p)$ ($p=3,4,5,cdots$) in the ferromagnetic gapless regime behaves qualitatively the same as in the noninteracting case ($Delta=0$) even in the weak electric field limit. When $Delta$ deviates from these values, the amplitude of the oscillation under a weak electric field is suppressed by a factor of the system size. We estimate the strength of the electric field required to observe such a behavior using the Landau--Zener formula.
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