Disentangling ( 2 + 1 ) D topological states of matter with entanglement negativity

• Published in: Physical review. B 2021-09, Vol.104 (11), p.1, Article 115155
• Main Authors: Lim, Pak Kau, Asasi, Hamed, Teo, Jeffrey C. Y., Mulligan, Michael
• Format: Article
• Language: English
• Subjects: CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Cylinders; Edge states; Entanglement; Entanglement measures; Fractional quantum Hall effect; Ground state; Materials Science; Mathematical analysis; Physics; Quantum entanglement; Tensors; Topological phases of matter; Topology; Toruses; Wave functions
• ISSN: 2469-9950; 2469-9969
• DOI: 10.1103/PhysRevB.104.115155

We use the entanglement negativity, a bipartite measure of entanglement in mixed quantum states, to study how multipartite entanglement constrains the real-space structure of the ground-state wave functions of ( 2 + 1 ) -dimensional topological phases. We focus on the (Abelian) Laughlin and (non-Abelian) Moore-Read states at filling fraction ν = 1 / m . We show that a combination of entanglement negativities, calculated with respect to specific cylinder and torus geometries, determines a necessary condition for when a topological state can be disentangled, i.e., factorized into a tensor product of states defined on cylinder subregions. This condition, which requires the ground state to lie in a definite topological sector, is sufficient for the Laughlin state. On the other hand, we find that a general Moore-Read ground state cannot be disentangled even when the disentangling condition holds.