  Novel critical phenomena beyond the Landau-Ginzburg-Wilson paradigm have been
long sought after. Among many candidate scenarios, the deconfined quantum
critical point (DQCP) constitutes the most fascinating one, and its lattice
model realization has been debated over the past two decades. Here we apply the
spherical Landau level regularization upon the exact (2+1)D SO(5) non-linear
sigma model with a topological term to study the potential DQCP therein. We
perform density matrix renormalization group (DMRG) simulation with
SU(2)$_\mathrm{spin}\times$U(1)$_\mathrm{charge}\times$U(1)$_\mathrm{angular-momentum}$
symmetries explicitly implemented. Using crossing point analysis for the
critical properties of the DMRG data, accompanied by quantum Monte Carlo
simulations, we accurately obtain the comprehensive phase diagram of the model
and find various novel quantum phases, including N\'eel, ferromagnet (FM),
valence bond solid (VBS), valley polarized (VP) states and a gapless quantum
disordered phase occupying extended area of the phase diagram. The VBS-Disorder
and N\'eel-Disorder transitions are continuous with non-Wilson-Fisher
exponents. Our results show the VBS and N\'eel states are separated by either a
weakly first-order transition or the disordered region with a multicritical
point in between, thus opening up more interesting questions on the two-decade
long debate on the nature of DQCP.
