The deconfined quantum critical point (DQCP) is an example of phase transitions beyond the Landau symmetry-breaking paradigm that attracts wide interest. However, its nature has not been settled after decades of study. In this paper, we apply the recently proposed fuzzy-sphere regularization to study the SO(5) nonlinear sigma model with a topological Wess-Zumino-Witten term, which serves as a dual description of the DQCP with an exact SO(5) symmetry. We demonstrate that the fuzzy sphere functions as a powerful microscope, magnifying and revealing a wealth of crucial information about the DQCP, ultimately paving the way toward its final answer. In particular, through exact diagonalization, we provide clear evidence that the DQCP exhibits approximate conformal symmetry. The evidence includes the existence of a conserved SO(5) symmetry current, a stress tensor, and integer-spaced levels between conformal primaries and their descendants. Most remarkably, we identify 23 primaries and 76 conformal descendants. Furthermore, by examining the renormalization group flow of the lowest symmetry singlet as well as other primaries, we provide numerical evidence in favor of DQCP being pseudo-critical, with the approximate conformal symmetry plausibly emerging from nearby complex fixed points. The primary spectrum we compute also has important implications, including the conclusion that the SO(5) DQCP cannot describe a direct transition from the Néel to valence bond solid phase on the honeycomb lattice.

中文翻译：

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SO(5) 模糊球显微镜下的去限制相变：近似共形对称性、伪临界性和算子谱


解禁量子临界点（DQCP）是超越朗道对称破缺范式的相变示例，引起了广泛的兴趣。然而，经过数十年的研究，其本质仍未得到解决。在本文中，我们应用最近提出的模糊球正则化来研究具有拓扑 Wess-Zumino-Witten 项的 SO(5) 非线性 sigma 模型，该模型作为具有精确 SO(5) 对称性的 DQCP 的对偶描述。我们证明了模糊球体就像一个强大的显微镜，放大并揭示了有关 DQCP 的大量关键信息，最终为其最终答案铺平了道路。特别是，通过精确对角化，我们提供了明确的证据表明 DQCP 表现出近似共形对称性。证据包括存在保守的 SO(5) 对称电流、应力张量以及共形原色及其后代之间的整数间隔能级。最值得注意的是，我们确定了 23 个初代和 76 个适形后代。此外，通过检查最低对称性单重态以及其他原色的重正化群流，我们提供了支持 DQCP 伪临界的数值证据，近似共角对称似乎从附近的复杂固定点出现。我们计算的主光谱也具有重要意义，包括 SO(5) DQCP 无法描述蜂窝晶格上从尼尔固相到价键固相的直接转变的结论。