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PreprintCC BY 4.0arXiv

Strong Symmetry from Two-Point Correlations

  • Han Yan
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Abstract

Strong and weak symmetries and their spontaneous breaking distinguish different forms of symmetry and order in mixed states. We show that complete one- and two-point correlation functions, equivalently all two-site reduced density matrices, determine exact strong symmetry for continuous onsite unitary actions of connected groups: states with identical correlations have the same strong symmetry and character. We also present an algorithm to determine the maximal connected strong-symmetry sub-Lie group and its character from two-point correlations. Because such correlations are more accessible than full-state tomography, the algorithm is readily applicable to experiments ranging from condensed-matter systems to quantum simulators and circuits. We also identify group and representation-specific cases in which fewer correlations suffice.

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Cite

BibTeXRIS
BibTeX
@misc{yan2026strong,
  title = {{Strong Symmetry from Two-Point Correlations}},
  author = {Han Yan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23591},
  eprint = {2609.23591},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23591},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Strong Symmetry from Two-Point Correlations
AU  - Han Yan
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23591
UR  - https://arxiv.org/abs/2609.23591
AB  - Strong and weak symmetries and their spontaneous breaking distinguish different forms of symmetry and order in mixed states. We show that complete one- and two-point correlation functions, equivalently all two-site reduced density matrices, determine exact strong symmetry for continuous onsite unitary actions of connected groups: states with identical correlations have the same strong symmetry and character. We also present an algorithm to determine the maximal connected strong-symmetry sub-Lie group and its character from two-point correlations. Because such correlations are more accessible than full-state tomography, the algorithm is readily applicable to experiments ranging from condensed-matter systems to quantum simulators and circuits. We also identify group and representation-specific cases in which fewer correlations suffice.
ER  -