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

Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: multicritical point and disorder phase