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arXiv · 2601.23078

Mermin-Wagner theorems for quantum systems with multipole symmetries

Timo Feistl·Severin Schraven·Simone Warzel
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Abstract

We prove Mermin-Wagner-type theorems for quantum lattice systems in the presence of multipole symmetries. These theorems show that the presence of higher-order symmetries protects against the breaking of lower-order ones. In particular, we prove that the critical dimension in which the charge symmetry can be broken increases if the system admits higher multipole symmetries, e.g. $ d = 4 $ on the regular lattice $ \mathbb{Z}^d $ in the presence of dipole symmetry.

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Timo Feistl, Severin Schraven, Simone Warzel. 2026-01-30. Mermin-Wagner theorems for quantum systems with multipole symmetries. https://arxiv.org/abs/2601.23078

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