Strong Symmetry from Two-Point Correlations

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.

Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th)

arXiv:2609.23591 [quant-ph]

(or arXiv:2609.23591v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.23591 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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