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arXiv:2311.18091 · Physical Review A

Relaxation in dipolar spin ladders: From pair production to false-vacuum decay

G. A. Domínguez‐Castro, Thomas Bilitewski, David Wellnitz, Ana María Rey, Luis Santos

Published Aug 15, 2024• 5 citations
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Abstract

The authors demonstrate how the interplay between intrachain and interchain interactions in a dipolar spin chain results in three distinct relaxation regimes: ergodic, characterized by rapid relaxation towards equilibrium; metastable, where the state is quasi-localized; and partially relaxed, exhibiting both partial ergodic and quasi-localized behaviors simultaneously.

DOI
10.1103/physreva.110.l021302

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The authors demonstrate how the interplay between intrachain and interchain interactions in a dipolar spin chain results in three distinct relaxation regimes: ergodic, characterized by rapid relaxation towards equilibrium; metastable, where the state is quasi-localized; and partially relaxed, exhibiting both partial ergodic and quasi-localized behaviors simultaneously.
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In this work we characterize the false vacuum decay in the ferromagnetic quantum Ising chain with a weak longitudinal field subject to continuous monitoring of the local magnetization. Initializing the system in a metastable state, the false vacuum, we study the competition between coherent dynamics, which tends to create resonant bubbles of the true vacuum, and measurements which induce heating and reduce the amount of quantum correlations. To this end we exploit a numerical approach based on the combination of matrix product states with stochastic quantum trajectories which allows for the simulation of the trajectory-resolved non-equilibrium dynamics of interacting many-body systems in the presence of continuous measurements. We show how the presence of measurements affects the false vacuum decay: At short times the departure from the local minimum is accelerated while at long times the system thermalizes to an infinite-temperature incoherent mixture. For large measurement rates the system enters a quantum Zeno regime. The false vacuum decay and the thermalization physics are characterized in terms of the magnetization, connected correlation function, and the trajectory-resolved entanglement entropy.
We study scattering in the quantum Ising model in two dimensions. In the ordered phase, the spectrum contains a ladder of bound states and intertwined scattering resonances, which enable various scattering channels. By preparing wave packets on a 24 × 24 lattice and evolving the state with tensor networks, we explore and characterize these regimes, ranging from elastic scattering in the perturbative regime, to non-perturbative processes closer to the critical point. Then, we break the spin inversion symmetry and study the stability of the metastable false vacuum state on the collision of its excitations. We find that a highly-energetic scattering process can induce a violent decay of the false vacuum, and investigate the spread of the resulting true vacuum bubble. Spin chains enable quantum simulation of scattering-related phenomena of interest for highenergy- and condensed-matter-physics, yet current approaches are limited to low dimensional cases. Here, the authors address this gap by studying magnon scattering in 2D quantum Ising models via tree tensor networks. This unveils new resonances and induced false vacuum decay dynamics.
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