Abstract
Integrable models are characterized by the existence of stable excitations that can propagate indefinitely without decaying. This includes multimagnon bound states in the celebrated spin-chain model and its integrable Floquet counterpart. A recent Google Quantum AI experiment [A. Morvan et al., Nature 612, 240 (2022)] realizing the Floquet model has demonstrated the persistence of such collective excitations even when the integrability is broken: this observation is at odds with the expectation of ergodic dynamics in generic nonintegrable systems. Here, we study the spectrum of the model realized in the experiment using exact diagonalization and physical arguments. We find that isolated bands corresponding to the descendants of the exact bound states of the integrable model are clearly observable in the spectrum for a large range of system sizes. However, our numerical analysis of the localization properties of the eigenstates suggests that the bound states become unstable in the thermodynamic limit. A perturbative estimate of the decay rate agrees with the prediction of an eventual instability for large system sizes.
- Received 28 August 2023
- Revised 1 December 2023
- Accepted 23 January 2024
DOI:https://doi.org/10.1103/PRXQuantum.5.010317
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
In a recent experiment, the Google Quantum AI collaboration explored the intriguing behavior of interacting microwave photons forming multiphoton lumps within a periodic quantum circuit, challenging our understanding of nonintegrable systems. The experimental observation suggested such stable particles, contrary to typical expectations of decay. Our work unravels the mystery, disclosing that while these collective states are distinctly visible in the spectrum for various system sizes, they eventually succumb to instability in large enough systems.
Our analysis focuses on the spectrum of the model with three particles arranged in a decorated ring geometry. As we examine larger system sizes, we find a gradual decrease in the “boundedness” of the three particles within the seemingly robust collective states, suggesting an eventual instability. This conclusion finds support in a perturbative analysis, revealing a small but finite decay rate. Notably, our estimates suggest that the experiment’s timescales and sizes, along with previous numerical simulations, are smaller by 1 or more orders of magnitude compared to where the decay of bound states would manifest in dynamical signatures.
