Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact ground state for the four-electron problem in a 2D finite
  honeycomb lattice   Working in a subspace with dimensionality much smaller than the dimension of
the full Hilbert space, we deduce exact 4-particle ground states in 2D samples
containing hexagonal repeat units and described by Hubbard type of models. The
procedure identifies first a small subspace ${\cal{S}}$ in which the ground
state $|\Psi_g\rangle$ is placed, than deduces $|\Psi_g\rangle$ by exact
diagonalization in ${\cal{S}}$. The small subspace is obtained by the repeated
application of the Hamiltonian $\hat H$ on a carefully chosen starting wave
vector describing the most interacting particle configuration, and the wave
vectors resulting from the application of $\hat H$, till the obtained system of
equations closes in itself. The procedure which can be applied in principle at
fixed but arbitrary system size and number of particles, is interesting by its
own since provides exact information for the numerical approximation techniques
which use a similar strategy, but apply non-complete basis for ${\cal{S}}$. The
diagonalization inside ${\cal{S}}$ provides an incomplete image about the low
lying part of the excitation spectrum, but provides the exact $|\Psi_g\rangle$.
Once the exact ground state is obtained, its properties can be easily analyzed.
The $|\Psi_g\rangle$ is found always as a singlet state whose energy,
interestingly, saturates in the $U \to \infty$ limit. The unapproximated
results show that the emergence probabilities of different particle
configurations in the ground state present "Zittern" (trembling)
characteristics which are absent in 2D square Hubbard systems. Consequently,
the manifestation of the local Coulomb repulsion in 2D square and honeycomb
types of systems presents differences, which can be a real source in the
differences in the many-body behavior.

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The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci