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

Jun 14, 2021

35 pages

Published in:

Phys.Rev.B 104 (2021) 11, 115155

Published: Sep 15, 2021

e-Print:

2106.07668 [cond-mat.str-el]

DOI:

10.1103/PhysRevB.104.115155 (publication)

View in:

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Abstract: (APS)

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.

Note:

35 pages, 5 figures

phase: topological
geometry: torus
entanglement
ground state
cylinder
abelian
nonabelian
dimension: 3

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