Designs without disorder: unitary k-designs from a single-site bulk defect

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.

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BibTeX RIS

BibTeX

@misc{sur2026designs,
  title = {{Designs without disorder: unitary $k$-designs from a single-site bulk defect}},
  author = {Samudra Sur and Pratik Nandy},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16140},
  eprint = {2609.16140},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16140},
}

RIS

TY  - UNPB
TI  - Designs without disorder: unitary k-designs from a single-site bulk defect
AU  - Samudra Sur
AU  - Pratik Nandy
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.16140
UR  - https://arxiv.org/abs/2609.16140
AB  - 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.
ER  -

Abstract

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