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This research demonstrates that a minimal local defect can induce approximate unitary $k$-designs within integrable quantum many-body systems, effectively bridging the gap between ordered and chaotic regimes. By deriving analytical selection rules for Pauli kick protocols, the study provides a scalable method to generate randomness essential for quantum simulation and error correction without requiring full system chaos. The findings confirm that this design-forming mechanism persists even as system size increases, offering a robust pathway for engineering quantum resources in constrained environments.
Designs without disorder: unitary $k$-designs from a single-site bulk defect
arXiv:2609.16140v1 Announce Type: new Abstract: We show that an $O(1)$ local defect is sufficient to generate approximate unitary $k$-designs from an otherwise integrable quantum many-body system. Using a two-Pauli-kick (2PK) protocol with temporal sampling, we demonstrate this mechanism in a fixed-magnetization sector of deterministic XXZ spin chains with a single integrability-breaking bulk defect. We derive an analytical selection rule for the Pauli kicks and show that symmetry-preserving strings with a specific domain-wall count, fixed by the couplings, govern design formation. An exhaustive search over all admissible Pauli strings identifies a broad family of kicks that produce designs in the chaotic regime, whereas no such kicks exist in the integrable limit, including for boundary defects. We further show that the design-forming mechanism remains effective for weak bulk defects as the system size increases.
Abstract:We show that an $O(1)$ local defect is sufficient to generate approximate unitary $k$-designs from an otherwise integrable quantum many-body system. Using a two-Pauli-kick (2PK) protocol with temporal sampling, we demonstrate this mechanism in a fixed-magnetization sector of deterministic XXZ spin chains with a single integrability-breaking bulk defect. We derive an analytical selection rule for the Pauli kicks and show that symmetry-preserving strings with a specific domain-wall count, fixed by the couplings, govern design formation. An exhaustive search over all admissible Pauli strings identifies a broad family of kicks that produce designs in the chaotic regime, whereas no such kicks exist in the integrable limit, including for boundary defects. We further show that the design-forming mechanism remains effective for weak bulk defects as the system size increases.
Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th)
arXiv:2609.16140 [quant-ph]
(or arXiv:2609.16140v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.16140 arXiv-issued DOI via DataCite (pending registration)
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