In the absence of spin-orbit coupling, the conventional dogma of Anderson localization asserts that all states localize in two dimensions, with a glaring exception: the quantum Hall plateau transition (QHPT). In that case, the localization length diverges and interference-induced quantum-critical spatial fluctuations appear at all length scales. Normally QHPT states occur only at isolated energies; accessing them therefore requires fine-tuning of the electron density or magnetic field. In this paper we show that QHPT states can be realized throughout an energy continuum, i.e. as an "energy stack" of critical states wherein each state in the stack exhibits QHPT phenomenology. The stacking occurs at the surface of a class AIII topological phase, where it is protected by U(1) and (anomalous) chiral or time-reversal symmetries. Spectrum-wide criticality is diagnosed by comparing numerics to universal results for the longitudinal Landauer conductance and wave function multifractality at the QHPT. Results are obtained from an effective 2D surface field theory and from a bulk 3D lattice model. We demonstrate that the stacking of quantum-critical QHPT states is a robust phenomenon that occurs for AIII topological phases with both odd and even winding numbers. The latter conclusion may have important implications for the still poorly-understood logarithmic conformal field theory believed to describe the QHPT.

中文翻译：

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AIII类拓扑相表面的全光谱量子临界性：整数量子霍尔高原跃迁的“能量堆栈”

在没有自旋轨道耦合的情况下，安德森定位的传统教条断言，所有状态都在二维内定位，但有一个明显的例外：量子霍尔高原跃迁（QHPT）。在这种情况下，定位长度会发散，并且在所有长度尺度上都会出现干扰引起的量子临界空间波动。通常，QHPT状态仅在孤立的能量处发生；因此，访问它们需要对电子密度或磁场进行微调。在本文中，我们表明QHPT状态可以在整个能量连续体中实现，即作为临界状态的“能量堆栈”，其中堆栈中的每个状态都表现出QHPT现象。堆叠发生在AIII类拓扑阶段的表面，在那里受到U（1）和（异常）手性或时间反转对称性的保护。通过将数值与QHPT的纵向Landauer电导和波函数多重分形的通用结果进行比较，可以诊断整个光谱的临界度。从有效的2D表面场理论和体3D晶格模型获得结果。我们证明了量子临界QHPT态的堆积是一个鲁棒的现象，对于奇数和偶数绕组数的AIII拓扑相都会发生。后一个结论可能对仍然难以理解的对数共形场理论（可能描述QHPT）具有重要意义。我们证明了量子临界QHPT态的堆积是一个鲁棒的现象，对于奇数和偶数绕组数的AIII拓扑相都会发生。后一个结论可能对仍然难以理解的对数共形场理论（可能描述QHPT）具有重要意义。我们证明了量子临界QHPT态的堆积是一个鲁棒的现象，对于奇数和偶数绕组数的AIII拓扑相都会发生。后一个结论可能对仍然难以理解的对数共形场理论（可能描述QHPT）具有重要意义。