  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. Following the
pioneering works with the fuzzy sphere methods [W. Zhu, et al, Phys. Rev. X 13,
021009], we apply the spherical Landau level regularization to study the
effective (2+1)D SO(5) non-linear sigma model with a topological term and the
potential DQCP therein. Utilizing the state-of-the-art density matrix
renormalization group method with explicit
$\text{SU(2)}_\text{spin}\times\text{U(1)}_\text{charge}\times\text{U(1)}_\text{angular-momentum}$
symmetry as well as exact diagonalization simulations, we provide a
comprehensive phase diagram for the model with a SO(5) continuous transition
line -- extension of the previous identified SO(5) multicritical point
[arXiv:2307.05307] -- while tuning interaction length. The state-operator
correspondence with the conformal tower structure is used to identify the
emergent conformal symmetry with the best scaling dimension of relevant primary
fields and they match well with the critical exponents obtained from the
crossing point analysis of the correlation ratio. Our results thus further
support the rich structure of the phase diagram of the SO(5) model.
