论文标题
高阶拓扑相变的Fracton临界点
Fracton Critical Point in Higher-Order Topological Phase Transition
论文作者
论文摘要
量子相变的理论在零温度下以不同的对称模式分开不同相的理论是现代量子多体物理学的基础之一。在本文中，我们证明了高阶拓扑绝缘子（HOTI）和具有相同对称性的微不足道的绝缘子之间存在2D拓扑相变的存在。我们提出了由HOTI和琐碎的Mott绝缘体区域之间的域壁的波动和渗透驱动的量子临界点（QCP）的理论。由于Spinon零模式装饰了域壁的粗糙角，相边界的波动触发了带有法acton动力学的Spinon-Dipole跳跃项。因此，我们发现QCP的特征是具有子系统$ u（1）$对称性的关键偶极液体理论，以及表现出对数增强功能的区域法律纠缠熵的分解：$ l \ ln（l）$。使用密度矩阵重新归一化组（DMRG）方法，我们在QCP处分析了偶极刚度以及结构因子，这为临界偶极子液体提供了具有玻色表面的临界偶极液。这些数值特征进一步支持QCP的分裂动力学，并为2D量子关键率与拓扑阶段相关的新范式。
The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this paper we demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. We present a theory of this quantum critical point (QCP) driven by the fluctuations and percolation of the domain walls between a HOTI and a trivial Mott insulator region. Due to the spinon zero modes that decorate the rough corners of the domain walls, the fluctuations of the phase boundaries trigger a spinon-dipole hopping term with fracton dynamics. Hence we find the QCP is characterized by a critical dipole liquid theory with subsystem $U(1)$ symmetry and the breakdown of the area law entanglement entropy which exhibits a logarithmic enhancement: $L \ln(L)$. Using the density matrix renormalization group (DMRG) method, we analyze the dipole stiffness together with structure factor at the QCP which provide strong evidence of a critical dipole liquid with a Bose surface. These numerical signatures further support the fracton dynamics of the QCP, and suggest a new paradigm for 2D quantum criticality proximate to a topological phase.
