Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Knot Topology in Quantum Spin System   Knot theory provides a powerful tool for the understanding of topological
matters in biology, chemistry, and physics. Here knot theory is introduced to
describe topological phases in the quantum spin system. Exactly solvable models
with long-range interactions are investigated, and Majorana modes of the
quantum spin system are mapped into different knots and links. The topological
properties of ground states of the spin system are visualized and characterized
using crossing and linking numbers, which capture the geometric topologies of
knots and links. The interactivity of energy bands is highlighted. In gapped
phases, eigenstate curves are tangled and braided around each other forming
links. In gapless phases, the tangled eigenstate curves may form knots. Our
findings provide an alternative understanding of the phases in the quantum spin
system, and provide insights into one-dimension topological phases of matter.

31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph