Emergent Conformal Symmetry at the Multicritical Point of (2+1)D SO(5) Model with Wess-Zumino-Witten Term on Sphere

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 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 SU(2)_spin×U(1)_charge×U(1)_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 pave the way to a definitive answer of the two-decade debate on this model.