Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classifying phases protected by matrix product operator symmetries using
  matrix product states   We classify the different ways in which matrix product states (MPS) can
transform under the action of matrix product operator (MPO) symmetries. We give
a local characterization of MPS tensors that generate ground spaces which
remain invariant under a global MPO symmetry and generally correspond to
symmetry breaking phases. This allows us to derive a set of quantities,
satisfying the so-called coupled pentagon equations, invariant under continuous
deformations of the MPS tensor, which provides the invariants to detect
different gapped phases protected by MPO symmetries. Our result matches the
TQFT classification of gapped boundaries in terms of module categories of
fusion categories. However, our techniques extend the classification beyond
renormalization fixed points and facilitates the numerical study of these
systems. When the MPO symmetries form a global onsite representation of a
group, we recover the symmetry protected topological order classification for
unique and degenerate ground states. For MPO symmetries that are non-onsite
representations of groups, we obtain restrictions on the possible ground state
degeneracies depending both on the group and on the concrete form of the MPO
representation, as opposed to depend just on the group as in the onsite case.
Moreover, we study the interplay between time reversal symmetry and an MPO
symmetry and we also provide examples of our classification together with
explicit constructions of MPO and MPS based on groups. Finally, we elaborate on
the connection between our setup and gapped boundaries of two-dimensional
topological systems, where MPO symmetries also play a key role.

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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th