Spectrum-wide quantum criticality at the surface of class AIII topological phases: An "energy stack" of integer quantum Hall plateau transitions

TL;DR

This paper demonstrates that quantum Hall plateau transition states can occur across an entire energy spectrum on the surface of class AIII topological phases, forming an 'energy stack' of critical states protected by symmetries.

Contribution

It introduces the concept of spectrum-wide quantum criticality at the surface of AIII topological phases, showing the stacking of quantum Hall transition states without fine-tuning.

Findings

Quantum critical states form an energy continuum on the surface of AIII topological phases.

Stacking of quantum Hall plateau transition states is robust across different winding numbers.

Spectrum-wide criticality is confirmed by numerical and theoretical analysis.

Abstract

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 without fine-tuning 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.