Mechanism of defect formation in the quantum annealing of random transverse-field Ising chain

• URL: http://arxiv.org/abs/2505.20204v1
• Date: Mon, 26 May 2025 16:44:51 GMT
• Title: Mechanism of defect formation in the quantum annealing of random transverse-field Ising chain
• Authors: Róbert Juhász,
• Abstract summary: A microscopic mechanism of defect formation in the quantum annealing of the random transverse-field Ising chain is proposed.<n>The ferromagnetic ground states of clusters are either preserved or get excited in pairwise fusions of clusters.<n>An interesting consequence of the theory is that, although the Griffiths-McCoy phases surrounding the critical point are gapless, these phases are still effectively gapped.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Based on the strong-disorder renormalization group method, a microscopic mechanism of defect formation in the quantum annealing of the random transverse-field Ising chain is proposed, which represents the annealing process as a gradual aggregation of strongly coupled spin clusters. The ferromagnetic ground states of clusters are either preserved or get excited in pairwise fusions of clusters, depending on the effective annealing rate of the fusion, the latter events being responsible for the appearance of defects in the final state. An interesting consequence of the theory is that, although the Griffiths-McCoy phases surrounding the critical point are gapless, these phases are still effectively gapped from the point of view of quantum annealing. Thereby we provide an a posteriori justification of the assumption on the finiteness of gap outside of the critical point tacitly used in earlier works, and also refine the functional form of its vanishing at the critical point. The defect density in the final state is found to decrease with the annealing time $\tau$ asymptotically as $n(\tau)\sim \ln^{-2}\left(\frac{\tau}{\ln^2\tau}\right)$. In addition to this, our approach gives access also to the time-dependent density of defects accumulated during the annealing process at intermediate times.

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