Extrinsic Geometry and Gappable Edges in Rotationally Invariant Topological Phases

Fuente: arXiv
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Main Authors: Sinha, Sounak, Bradlyn, Barry
Format: Preprint
Published: 2025
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author Sinha, Sounak
Bradlyn, Barry
author_facet Sinha, Sounak
Bradlyn, Barry
contents Recent work on Abelian topological phases with rotational symmetry has raised the question of whether rotational symmetry can protect gapless propagating edge modes. Here we address this issue by considering the coupling of topological phases to the extrinsic geometry of the background. First, we analyze an effective hydrodynamic theory for an Abelian topological phase with vanishing Hall conductance. After integrating out the bulk hydrodynamic degrees of freedom, we identify charge neutral, rotationally invariant mass terms by coupling the propagating boundary modes to the extrinsic geometry. This allows us to integrate out the edge modes and we find a gapped theory described by a local induced action that depends on the extrinsic geometry of the boundary, regardless of the shift. Finally, we apply these ideas to a microscopic theory and find the explicit bulk terms which respect gauge and rotational symmetry and open a gap in the edge spectrum.
format Preprint
id arxiv_https___arxiv_org_abs_2503_14267
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Extrinsic Geometry and Gappable Edges in Rotationally Invariant Topological Phases
Sinha, Sounak
Bradlyn, Barry
Mesoscale and Nanoscale Physics
Strongly Correlated Electrons
High Energy Physics - Theory
Recent work on Abelian topological phases with rotational symmetry has raised the question of whether rotational symmetry can protect gapless propagating edge modes. Here we address this issue by considering the coupling of topological phases to the extrinsic geometry of the background. First, we analyze an effective hydrodynamic theory for an Abelian topological phase with vanishing Hall conductance. After integrating out the bulk hydrodynamic degrees of freedom, we identify charge neutral, rotationally invariant mass terms by coupling the propagating boundary modes to the extrinsic geometry. This allows us to integrate out the edge modes and we find a gapped theory described by a local induced action that depends on the extrinsic geometry of the boundary, regardless of the shift. Finally, we apply these ideas to a microscopic theory and find the explicit bulk terms which respect gauge and rotational symmetry and open a gap in the edge spectrum.
title Extrinsic Geometry and Gappable Edges in Rotationally Invariant Topological Phases
topic Mesoscale and Nanoscale Physics
Strongly Correlated Electrons
High Energy Physics - Theory
url https://arxiv.org/abs/2503.14267