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arXiv · 2605.15200

Translation symmetry-enforced long-range entanglement in mixed states

Ryan Thorngren·Lei Gioia·Carolyn Zhang
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Abstract

We show by a counting argument that even though translation symmetry admits symmetric short-range entangled (SRE) eigenstates, there are not enough such SRE eigenstates to span the zero momentum sector. This means that the fixed point strong-to-weak spontaneous symmetry breaking state of translation symmetry is long-range entangled: it cannot be written as a mixture of SRE states. This is a subtle form of long-range entanglement in mixed states that cannot be detected by long-range connected correlation functions.

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Ryan Thorngren, Lei Gioia, Carolyn Zhang. 2026-05-14. Translation symmetry-enforced long-range entanglement in mixed states. https://arxiv.org/abs/2605.15200

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