球面上含Wess-Zumino-Witten项的(2+1)维SO(5)模型多临界点处的涌现共形对称性
Emergent Conformal Symmetry at the Multicritical Point of (2+1)D SO(5) Model with Wess-Zumino-Witten Term on Sphere
AI总结：
本研究采用球面朗道能级正则化结合密度矩阵重整化群与精确对角化方法，研究含拓扑项的(2+1)维SO(5)非线性σ模型，发现延伸的SO(5)连续相变线及涌现共形对称性，进一步丰富了该模型的相图结构。
摘要：
超越朗道-金兹堡-威尔逊（Landau-Ginzburg-Wilson）范式的新型临界现象长期以来一直是研究热点。在众多候选场景中，退禁闭量子临界点（deconfined quantum critical point, DQCP）是最引人关注的一类，其格点模型实现问题在过去二十年间一直存在争议。继采用模糊球面方法的先驱性工作[W. Zhu等人，Phys. Rev. X 13, 021009]之后，我们应用球面朗道能级正则化方法，研究含拓扑项的有效(2+1)维SO(5)非线性σ模型及其可能存在的DQCP。我们利用具备显式$\text{SU(2)}_\text{自旋}\times\text{U(1)}_\text{电荷}\times\text{U(1)}_\text{角动量}$对称性的先进密度矩阵重整化群方法，结合精确对角化模拟，给出了该模型的完整相图，其中包含一条SO(5)连续相变线——这是此前已识别的SO(5)多临界点[arXiv:2307.05307]的延伸——相变线通过调节相互作用长度得到。我们借助具有共形塔结构的态-算符对应关系识别涌现共形对称性，得到了相关初级场的最优标度维数，这些结果与通过关联比交叉点分析得到的临界指数吻合良好。我们的研究结果进一步佐证了SO(5)模型相图的丰富结构。
英文摘要：
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.
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