Entanglement in quantum theory is a peculiar concept to scientists. With
this concept we are forced to re-consider the cluster property which means that
one event is irrelevant to another event when they are fully far away. In the
recent works we showed that the quasi-degenerate states induce the violation of cluster property in antiferromagnets when the
continuous symmetry breaks spontaneously. We expect that the violation
of cluster property will be observed in other materials too, because the
spontaneous symmetry breaking is found in many systems such as the high
temperature superconductors and the superfluidity. In order to examine the
cluster property for these materials, we studied a quantum nonlinear sigma
model with U(1) symmetry in the previous work. There we showed that the model
does have quasi-degenerate states. In this paper we study the quantum nonlinear
sigma model with SU(2) symmetry. In our approach we first define the quantum
system on the lattice and then adopt the representation where the kinetic term
is diagonalized. Since we have no definition on the conjugate variable to the
angle variable, we use the angular momentum operators instead for the kinetic
term. In this representation we introduce the states with the fixed quantum
numbers and carry out numerical calculations using quantum Monte Carlo methods
and other methods. Through analytical and numerical studies, we conclude that
the energy of the quasi-degenerate state is proportional to the squared total
angular momentum as well as to the inverse of the lattice size.
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