Translation symmetry-enforced long-range entanglement in mixed states

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.

Source: arXiv:2605.15200v1 - http://arxiv.org/abs/2605.15200v1 PDF: https://arxiv.org/pdf/2605.15200v1 Original Link: http://arxiv.org/abs/2605.15200v1