  A local impurity usually only strongly affects few single-particle energy
levels, thus cannot induce a quantum phase transition (QPT), or any macroscopic
quantum phenomena in a many-body system within the Hermitian regime. However,
it may happen for a non-Hermitian impurity. We investigate the many-body ground
state property of a one-dimensional tight-binding ring with an embedded single
asymmetrical dimer based on exact solutions. We introduce the concept of
semi-localization state to describe a new quantum phase, which is a crossover
from extended to localized state. The peculiar feature is that the decay length
is of the order of the system size, rather than fixed as a usual localized
state. In addition, the spectral statistics is non-analytic as asymmetrical
hopping strengths vary, resulting a sudden charge of the ground state. The
distinguishing feature of such a QPT is that the density of ground state energy
varies smoothly due to unbroken symmetry. However, there are other observables,
such as the groundstate center of mass and average current, exhibit the
behavior of second-order QPT. This behavior stems from time-reversal symmetry
breaking of macroscopic number of single-particle eigen states.
