  From the perspective of low-lying excited states, we study the deconfined
quantum critical point (DQCP) in a one-dimensional quantum spin chain by means
of the entanglement entropy and fidelity. Our results show that there is a
close connection between the reconstruction of low-lying excitation spectra and
the DQCP. The precise position of the critical point and its continuous nature
is indicated by the singular behavior of the entanglement and fidelity of the
first-excited state. Furthermore, compared with the
Berezinskii-Kosterlitz-Thouless type phase transitions, which also go beyond
the scope of Landau-Ginzburg-Wilson paradigm, we attempt to reveal the essence
of different types of symmetries on both sides of the DQPT from different
manifestations of entanglement singularity.
