  The deconfined quantum critical point (DQCP) -- the enigmatic incarnation of
the quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm of
symmetries and their spontaneous breaking -- has been proposed and actively
pursued for more than two decades. Various 2D quantum many-body lattice models,
both in spin/boson and fermion representations have been tested with the
state-of-the-art numerical techniques and field-theoretical analyses, and yet,
the conclusion is still controversial. Experimental realizations of DQCP in the
quantum magnet SrCu$_2$(BO$_3$)$_2$ and superconducting quantum criticality in
2D material have either shown first order transition or intermediate phase. The
tension between the lattice scale details and the requirement from continuum
limit, manifested in the form of the inconsistent critical scaling behavior and
violations of generic conformal bootstrap bound, has not been resolved. Here we
solve these decades-long controversies from the new and fundamental perspective
of the quantum entanglement. We develop the incremental algorithm to compute
the entanglement entropy at a fermionic DQCP with unprecedentedly accurate data
and reveal the universal coefficient of the logarithmic correction therein is
negative and at odds with positivity requirement of the conformal field theory.
Together with results in other 2D DQCP lattice models (both in fermion and spin
systems), our discoveries clearly demonstrate the 2D SU(2) antiferromagnet to
valence bond solid DQCPs are not conformal fixed point and naturally explain
the experimental difficulties in finding them. This marks the end of the
beginning of unambiguous finding of the quantum phase transitions truely beyond
the Landau-Ginzburg-Wilson paradigm, since its suggestion two decades ago.
