Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological phases of fermions in one dimension   In this paper we show how the classification of topological phases in
insulators and superconductors is changed by interactions, in the case of 1D
systems. We focus on the TR-invariant Majorana chain (BDI symmetry class).
While the band classification yields an integer topological index $k$, it is
known that phases characterized by values of $k$ in the same equivalence class
modulo 8 can be adiabatically transformed one to another by adding suitable
interaction terms. Here we show that the eight equivalence classes are distinct
and exhaustive, and provide a physical interpretation for the interacting
invariant modulo 8. The different phases realize different Altland-Zirnbauer
classes of the reduced density matrix for an entanglement bipartition into two
half-chains. We generalize these results to the classification of all one
dimensional gapped phases of fermionic systems with possible anti-unitary
symmetries, utilizing the algebraic framework of central extensions. We use
matrix product state methods to prove our results.

16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg