Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Phase Transitions and Localization in Semigroup Fredkin Spin
  Chain   We construct an extended quantum spin chain model by introducing new degrees
of freedom to the Fredkin spin chain. The new degrees of freedom called arrow
indices are partly associated to the symmetric inverse semigroup $\cS^3_1$.
Ground states of the model fall into three different phases, and quantum phase
transition takes place at each phase boundary. One of the phases exhibits
logarithmic violation of the area law of entanglement entropy and quantum
criticality, whereas the other two obey the area law. As an interesting feature
arising by the extension, there are excited states due to disconnections with
respect to the arrow indices. We show that these states are localized without
disorder.

5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
19
The categories of this paper are: eess
3
The categories of this paper are: physics