论文标题
通过调整精确张量网络状态进行拓扑交叉量子相变
Topological fracton quantum phase transitions by tuning exact tensor network states
论文作者
论文摘要
物质的间隙阶段概括了拓扑顺序的概念，并扩大了我们对量子多体系统纠缠的基本理解。但是，他们的分析或数值描述超出了可解决的模型，仍然是一个巨大的挑战。在这里，我们采用了精确的3D量子张量 - 网络方法，使我们能够研究原型X Cube Fracton模型的$ \ MATHBB {Z} _n $概括及其通过完全拖动的波形波形变形之间的不同拓扑状态之间的量子相变。我们将（变形的）量子状态恰好映射到经典晶格仪理论和plaquette时钟模型的组合，并采用数值技术来计算各种纠缠顺序参数。对于$ \ mathbb {z} _n $型号，我们找到了（弱）一阶三局局部过渡的家族，在$ n \ to \ infty $的限制中，将$ n \ to \ infty $融合到Landau-Ginzburg-Wilson Paradigm之外的连续相变。我们还发现了一条3D共形量子临界点（带有临界磁通量回路波动）的线，该点在$ n \ to \ infty $限制中，似乎与无间隙的反构成的fracton状态共存。
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 $\mathbb{Z}_N$ generalization of the prototypical X cube fracton model and its quantum phase transitions between distinct topological states via fully tractable wavefunction 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 $\mathbb{Z}_N$ model we find a family of (weakly) first-order fracton confinement transitions that in the limit of $N\to\infty$ 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 $N\to\infty$ limit, appears to coexist with a gapless deconfined fracton state.
