Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two patterns of PT-symmetry breakdown in a non-numerical six-state
  simulation   Three-parametric family of non-Hermitian but ${\cal PT}-$symmetric six-by-six
matrix Hamiltonians $H^{(6)}(x,y,z)$ is considered. The ${\cal PT}-$symmetry
remains spontaneously unbroken (i.e., the spectrum of the bound-state energies
remains real so that the unitary-evolution stability of the quantum system in
question is shown guaranteed) in a non-empty domain ${\cal D}^{(physical)}$ of
parameters $x,y,z$. The construction of the exceptional-point (EP) boundary
$\partial{\cal D}^{(physical)}$ of the physical domain is preformed using an
innovative non-numerical implicit-function-construction strategy. The topology
of the resulting EP boundary of the spontaneous ${\cal PT}-$symmetry breakdown
(i.e., of the physical "horizon of stability") is shown similar to its much
more elementary $N=4$ predecessor. Again, it is shown to consist of two
components, viz., of the region of the quantum phase transitions of the first
kind (during which at least some of the energies become complex) and of the
quantum phase transitions of the second kind (during which some of the level
pairs only cross but remain real).

22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con