Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parafermionic phases with symmetry-breaking and topological order   Parafermions are the simplest generalizations of Majorana fermions that
realize topological order. We propose a less restrictive notion of topological
order in 1D open chains, which generalizes the seminal work by Fendley [J.
Stat. Mech., P11020 (2012)]. The first essential property is that the
groundstates are mutually indistinguishable by local, symmetric probes, and the
second is a generalized notion of zero edge modes which cyclically permute the
groundstates. These two properties are shown to be topologically robust, and
applicable to a wider family of topologically-ordered Hamiltonians than has
been previously considered. An an application of these edge modes, we formulate
a new notion of twisted boundary conditions on a closed chain, which guarantees
that the closed-chain groundstate is topological, i.e., it originates from the
topological manifold of degenerate states on the open chain. Finally, we
generalize these ideas to describe symmetry-breaking phases with a
parafermionic order parameter. These exotic phases are condensates of
parafermion multiplets, which generalizes Cooper pairing in superconductors.
The stability of these condensates are investigated on both open and closed
chains.

6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex