Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizing Topological Order with Matrix Product Operators   One of the most striking features of quantum phases that exhibit topological
order is the presence of long range entanglement that cannot be detected by any
local order parameter. The formalism of projected entangled-pair states is a
natural framework for the parameterization of the corresponding ground state
wavefunctions, in which the full wavefunction is encoded in terms of local
tensors. Topological order is reflected in the symmetries of these tensors, and
we give a characterization of those symmetries in terms of matrix product
operators acting on the virtual level. This leads to a set of algebraic rules
characterizing states with topological quantum order. The corresponding matrix
product operators fully encode all topological features of the theory, and
provide a systematic way of constructing topological states. We generalize the
conditions of $\mathsf{G}$ and twisted injectivity to the matrix product
operator case, and provide a complete picture of the ground state manifold on
the torus. As an example, we show how all string-net models of Levin and Wen
fit within this formalism, and in doing so provide a particularly intuitive
interpretation of the pentagon equation for F-symbols as the pulling of certain
matrix product operators through the string-net tensor network. Our approach
paves the way to finding novel topological phases beyond string-nets, and
elucidates the description of topological phases in terms of entanglement
Hamiltonians and edge theories.

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The categories of this paper are: hep-ph
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
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The categories of this paper are: hep-th