Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On topological phases of spin chains   Symmetry protected topological phases of one-dimensional spin systems have
been classified using group cohomology. In this paper, we revisit this problem
for general spin chains which are invariant under a continuous on-site symmetry
group G. We evaluate the relevant cohomology groups and find that the
topological phases are in one-to-one correspondence with the elements of the
fundamental group of G if G is compact, simple and connected and if no
additional symmetries are imposed. For spin chains with symmetry
PSU(N)=SU(N)/Z_N our analysis implies the existence of N distinct topological
phases. For symmetry groups of orthogonal, symplectic or exceptional type we
find up to four different phases. Our work suggests a natural generalization of
Haldane's conjecture beyond SU(2).

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The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio