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Topological Fracton Quantum Phase Transitions by Tuning Exact Tensor Network States
Physical Review Letters ( IF 8.1 ) Pub Date : 2023-05-25 , DOI: 10.1103/physrevlett.130.216704
Guo-Yi Zhu 1 , Ji-Yao Chen 2, 3 , Peng Ye 2, 4 , Simon Trebst 1
Affiliation  

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 ZN 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 ZN 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.

中文翻译:

通过调整精确张量网络状态实现拓扑分形量子相变

物质的有隙分形相概括了拓扑序的概念,并拓宽了我们对量子多体系统中纠缠的基本理解。然而,超出精确可解模型的分析或数值描述仍然是一个巨大的挑战。在这里,我们采用精确的 3D 量子张量网络方法,使我们能够研究Z通过完全可处理的波函数变形,对原型 X 立方分形模型及其不同拓扑状态之间的量子相变进行了推广。我们将(变形的)量子态精确地映射到经典晶格规范理论和平板时钟模型的组合,并采用数值技术来计算各种纠缠序参数。为了Z模型中我们发现了一系列(弱)一阶分形限制跃迁,其极限为无穷大收敛于朗道-金兹堡-威尔逊范式之外的连续相变。我们还发现了一条 3D 共形量子临界点线(具有临界磁通环波动),在无穷大极限,似乎与无间隙解约束分形状态共存。
更新日期:2023-05-26
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