Strong Symmetry from Two-Point Correlations
quant-ph, cond-mat.str-el, hep-th
Submitted: 2026-09-20
Updated: 2026-09-20
Comments: 6 pages, 1 figure
License: http://creativecommons.org/licenses/by/4.0/
The gist: Strong and weak symmetries and their spontaneous breaking distinguish different forms of symmetry and order in mixed states.
Terminology
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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