53 research outputs found
Edge theory approach to topological entanglement entropy, mutual information and entanglement negativity in Chern-Simons theories
We develop an approach based on edge theories to calculate the entanglement
entropy and related quantities in (2+1)-dimensional topologically ordered
phases. Our approach is complementary to, e.g., the existing methods using
replica trick and Witten's method of surgery, and applies to a generic spatial
manifold of genus , which can be bipartitioned in an arbitrary way. The
effects of fusion and braiding of Wilson lines can be also straightforwardly
studied within our framework. By considering a generic superposition of states
with different Wilson line configurations, through an interference effect, we
can detect, by the entanglement entropy, the topological data of Chern-Simons
theories, e.g., the -symbols, monodromy and topological spins of
quasiparticles. Furthermore, by using our method, we calculate other
entanglement measures such as the mutual information and the entanglement
negativity. In particular, it is found that the entanglement negativity of two
adjacent non-contractible regions on a torus provides a simple way to
distinguish Abelian and non-Abelian topological orders.Comment: 30 pages, 8 figures; Reference and discussions on double torus are
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Entanglement entropy of (3+1)D topological orders with excitations
Excitations in (3+1)D topologically ordered phases have very rich structures.
(3+1)D topological phases support both point-like and string-like excitations,
and in particular the loop (closed string) excitations may admit knotted and
linked structures. In this work, we ask the question how different types of
topological excitations contribute to the entanglement entropy, or
alternatively, can we use the entanglement entropy to detect the structure of
excitations, and further obtain the information of the underlying topological
orders? We are mainly interested in (3+1)D topological orders that can be
realized in Dijkgraaf-Witten gauge theories, which are labeled by a finite
group and its group 4-cocycle up to group
automorphisms. We find that each topological excitation contributes a universal
constant to the entanglement entropy, where is the quantum
dimension that depends on both the structure of the excitation and the data
. The entanglement entropy of the excitations of the
linked/unlinked topology can capture different information of the DW theory
. In particular, the entanglement entropy introduced by Hopf-link
loop excitations can distinguish certain group 4-cocycles from the
others.Comment: 12 pages, 4 figures; v2: minor changes, published versio
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