Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry and spontaneous symmetry breaking of the Hubbard model on a
  square lattice ground state   In this paper we consider the simplified form that a recently introduced
general operator description of the Hubbard model on the square lattice with
$N_a^2\gg 1$ sites, effective transfer integral $t$, and onsite repulsion $U$
has in a suitable one- and two-electron subspace. Such an operator description
is that consistent with the model exact global symmetry recently extended to
$SO(3)\times SO(3)\times U(1)$. There is a large consensus that in the
thermodynamic limit $N_a^2\rightarrow\infty$ long-range antiferromagnetic order
occurs in the spin-density $m=0$ ground state of the half-filled Hubbard model
on the square lattice. Here we find that the corresponding spontaneous symmetry
breaking lowers the symmetry of such a state from $SO(3)\times SO(3)\times
U(1)$ for $N_a^2\gg 1$ large but finite to $[U(2)\times U(1)]/Z_2^2 \equiv
[SO(3)\times U(1)\times U(1)]/Z_2$ for $N_a^2\rightarrow\infty$. Moreover, we
argue that the spin effective lattice being identical to the original lattice
is a necessary condition for the occurrence of ground-state long-range
antiferromagnetic order in the limit $N_a^2\rightarrow\infty$. Consistently,
strong evidence is provided that for very small hole concentration $0<x\ll1$
the ground state has a short-range incommensurate-spiral spin order. Our
results are of interest both for condensed-matter systems and ultra-cold
fermionic atoms on an optical square lattice.

36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph