Spectrum-Wide Quantum Criticality at the Surface of Class AIII Topological Phases: An “Energy Stack” of Integer Quantum Hall Plateau Transitions

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 sp...

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Autores principales:	Björn Sbierski, Jonas F. Karcher, Matthew S. Foster
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2020
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/aa01dc882b2d42149bd68c823141ec80
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spelling	oai:doaj.org-article:aa01dc882b2d42149bd68c823141ec802021-12-02T12:08:33ZSpectrum-Wide Quantum Criticality at the Surface of Class AIII Topological Phases: An “Energy Stack” of Integer Quantum Hall Plateau Transitions10.1103/PhysRevX.10.0210252160-3308https://doaj.org/article/aa01dc882b2d42149bd68c823141ec802020-05-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.10.021025http://doi.org/10.1103/PhysRevX.10.021025https://doaj.org/toc/2160-3308In 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.Björn SbierskiJonas F. KarcherMatthew S. FosterAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 10, Iss 2, p 021025 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Björn Sbierski Jonas F. Karcher Matthew S. Foster Spectrum-Wide Quantum Criticality at the Surface of Class AIII Topological Phases: An “Energy Stack” of Integer Quantum Hall Plateau Transitions
description	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.
format	article
author	Björn Sbierski Jonas F. Karcher Matthew S. Foster
author_facet	Björn Sbierski Jonas F. Karcher Matthew S. Foster
author_sort	Björn Sbierski
title	Spectrum-Wide Quantum Criticality at the Surface of Class AIII Topological Phases: An “Energy Stack” of Integer Quantum Hall Plateau Transitions
title_short	Spectrum-Wide Quantum Criticality at the Surface of Class AIII Topological Phases: An “Energy Stack” of Integer Quantum Hall Plateau Transitions
title_full	Spectrum-Wide Quantum Criticality at the Surface of Class AIII Topological Phases: An “Energy Stack” of Integer Quantum Hall Plateau Transitions
title_fullStr	Spectrum-Wide Quantum Criticality at the Surface of Class AIII Topological Phases: An “Energy Stack” of Integer Quantum Hall Plateau Transitions
title_full_unstemmed	Spectrum-Wide Quantum Criticality at the Surface of Class AIII Topological Phases: An “Energy Stack” of Integer Quantum Hall Plateau Transitions
title_sort	spectrum-wide quantum criticality at the surface of class aiii topological phases: an “energy stack” of integer quantum hall plateau transitions
publisher	American Physical Society
publishDate	2020
url	https://doaj.org/article/aa01dc882b2d42149bd68c823141ec80
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Spectrum-Wide Quantum Criticality at the Surface of Class AIII Topological Phases: An “Energy Stack” of Integer Quantum Hall Plateau Transitions

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