Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Absence of a critical nematic phase in the vicinity of the $\rm {SU}(3)$
  ferromagnetic point for the one-dimensional spin-1 bilinear-biquadratic model   The absence of a critical nematic phase in the vicinity of the $\rm {SU}(3)$
ferromagnetic point for the one-dimensional spin-1 bilinear-biquadratic model
is demonstrated by means of the tensor network algorithms. As it turns out, the
phase transition from the ferromagnetic phase to the dimerized phase at the
$\rm {SU}(3)$ ferromagnetic point is direct, but not of the first-order. The
transition point features highly degenerate ground states, which are scale but
not conformally invariant, with the fractal dimension being equal to 2. The
conceptual developments in effective field theories - the fractal dimension and
the counting rule of the Goldstone modes - play a pivotal role in clarifying
the numerical artifacts arising from the finiteness of the bond dimension in
the tensor network simulations, which are attributed to a proximity effect to a
highly entangled scale or conformally invariant ground state.

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The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph