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

TL;DR

This paper investigates a (2+1)D SO(5) model with a topological term, revealing an emergent conformal symmetry at a multicritical point through advanced numerical methods and phase diagram analysis.

Contribution

It applies spherical Landau level regularization and state-of-the-art numerical techniques to map the phase diagram and identify conformal symmetry at the multicritical point of the SO(5) model.

Findings

Identification of a continuous SO(5) transition line

Matching of critical exponents with conformal tower predictions

Support for the rich phase structure of the SO(5) model

Abstract

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.