Translation symmetry-enforced long-range entanglement in mixed states
Quantum Physics
2026-05-26 v3 Mesoscale and Nanoscale Physics
Strongly Correlated Electrons
Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2605.15200,
title = {Translation symmetry-enforced long-range entanglement in mixed states},
author = {Ryan Thorngren and Lei Gioia and Carolyn Zhang},
journal= {arXiv preprint arXiv:2605.15200},
year = {2026}
}
Comments
5+4 pages, 3 figures, v3: fixed typographical mistakes and updated a figure