Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energetical self-organization of a few strongly interacting particles   We study the quantum self-organization of a few interacting particles with
strong short-range interactions. The physical system is modelled via a 2D
Hubbard model with a nearest-neighbor interaction term of strength U and a
second nearest-neighbor hopping t. We find persistent many-body ground and
excited states whose structural properties are determined by the energetical
ordering occuring for vanishing hopping (t=0), when the self-organization of
the particles is determined by the interaction term only. For our analysis we
use the Euler characteristic of the network/graph grid structures formed by the
particles in real space (Fock states), which helps to quantify the energetical
ordering. We find multiple states, with integer Euler numbers whose values are
determined by the $t=0$ case, that persist/survive for $t \ne 0$ as long as the
interaction strength is large $U>>t$. The corresponding quantum phases contain
either density-wave-order (DWO) for low fillings or clustering-order (CO) for
high fillings. In addition, for the excited states we find superpositions of
Fock states whose probability amplitudes are self-tuned in a way that preserves
the integer value of the Euler characteristic from the $t=0$ case.

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The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th