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arXiv · 2605.28925

A local description of strong symmetries and strong-to-weak symmetry breaking in quantum many-body systems

Ruizhi Liu·Jinmin Yi·Dominic V. Else
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Abstract

In mixed states of quantum systems, symmetries come in two types: strong and weak. Furthermore, it has been argued that in quantum many-body systems, strong symmetries can be "spontaneously broken" down to weak symmetries. An issue is that as previously formulated, such "strong-to-weak symmetry breaking" appears to be a fairly non-local effect. In this paper, we show how to understand and diagnose strong symmetries and strong-to-weak symmetry breaking in an explicitly local way. Our main technical tool is a rigorous definition of strong symmetry in the limit of infinite volume, which generalizes the conventional finite-volume definitions, and for which we give several equivalent formulations, including one involving the concept of "local charge coherence". Finally, we introduce von Neumann systems, which in infinite-volume symmetries are intermediate between strong and weak symmetries. We derive a Lieb-Schultz-Mattis type anomaly constraint for von Neumann symmetries (and therefore, in particular, strong symmetries) in quantum spin chains.

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Ruizhi Liu, Jinmin Yi, Dominic V. Else. 2026-05-27. A local description of strong symmetries and strong-to-weak symmetry breaking in quantum many-body systems. https://arxiv.org/abs/2605.28925

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