Institute for Theoretical Physics, University of Cologne, Zülpicher Straße 77, 50937 Cologne, Germany.
Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, School of Physics, Sun Yat-sen University, Guangzhou, 510275, China.
Phys Rev Lett. 2023 May 26;130(21):216704. doi: 10.1103/PhysRevLett.130.216704.
Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems. However, their analytical or numerical description beyond exactly solvable models remains a formidable challenge. Here we employ an exact 3D quantum tensor-network approach that allows us to study a Z_{N} generalization of the prototypical X cube fracton model and its quantum phase transitions between distinct topological states via fully tractable wave function deformations. We map the (deformed) quantum states exactly to a combination of a classical lattice gauge theory and a plaquette clock model, and employ numerical techniques to calculate various entanglement order parameters. For the Z_{N} model we find a family of (weakly) first-order fracton confinement transitions that in the limit of N→∞ converge to a continuous phase transition beyond the Landau-Ginzburg-Wilson paradigm. We also discover a line of 3D conformal quantum critical points (with critical magnetic flux loop fluctuations) which, in the N→∞ limit, appears to coexist with a gapless deconfined fracton state.
物质的间隙分数量子相推广了拓扑序的概念，拓宽了我们对量子多体系统中纠缠的基本理解。然而，超越精确可解模型对其进行分析或数值描述仍然是一个艰巨的挑战。在这里，我们采用了一种精确的 3D 量子张量网络方法，该方法允许我们通过完全可处理的波函数变形来研究原型 X 立方体分数量子相及其在不同拓扑态之间的量子相变的 Z_{N}推广。我们将（变形的）量子态精确映射到经典格子规范理论和 plaquette 时钟模型的组合，并采用数值技术计算各种纠缠序参量。对于 Z_{N}模型，我们发现了一系列（弱）一级分数量子禁闭相变，在 N→∞的极限下，这些相变收敛到超越朗道-金兹堡-威尔逊范式的连续相变。我们还发现了一系列 3D 共形量子临界点（具有临界磁通量环涨落），在 N→∞的极限下，这些临界点似乎与无间隙的离域分数量子相共存。
