A counting argument proves insufficient symmetric short-range entangled states exist to span the zero-momentum sector, implying the translation-symmetric mixed state at the strong-to-weak symmetry breaking fixed point is long-range entangled.
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Translation symmetry-enforced long-range entanglement in mixed states
A counting argument proves insufficient symmetric short-range entangled states exist to span the zero-momentum sector, implying the translation-symmetric mixed state at the strong-to-weak symmetry breaking fixed point is long-range entangled.