Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fermionic Matrix Product States and One-Dimensional Topological Phases   We develop the formalism of fermionic matrix product states (fMPS) and show
how irreducible fMPS fall in two different classes, related to the different
types of simple $\mathbb{Z}_2$ graded algebras, which are physically
distinguished by the absence or presence of Majorana edge modes. The local
structure of fMPS with Majorana edge modes also implies that there is always a
two-fold degeneracy in the entanglement spectrum. Using the fMPS formalism we
make explicit the correspondence between the $\mathbb{Z}_8$ classification of
time-reversal invariant spinless superconductors and the modulo 8 periodicity
in the representation theory of real Clifford algebras. Studying fMPS with
general on-site unitary and anti-unitary symmetries allows us to define
invariants that label symmetry-protected phases of interacting fermions. The
behavior of these invariants under stacking of fMPS is derived, which reveals
the group structure of such interacting phases.We also consider spatial
symmetries and show how the invariant phase factor in the partition function of
reflection symmetric phases on an unorientable manifold appears in the fMPS
framework.

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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: math
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg