Partition Functions and Stability Criteria of Topological Insulators

Abstract

The non-chiral edge excitations of quantum spin Hall systems and topological insulators are described by means of their partition function. The stability of topological phases protected by time-reversal symmetry is rediscussed in this context and put in relation with the existence of discrete anomalies and the lack of modular invariance of the partition function. The ${\mathbb{Z}}_2$ characterization of stable topological insulators is extended to systems with interacting and non-Abelian edge excitations.

41 pages, 7 figures

References in corpus (12)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• The Quantum Spin Hall Effect: Theory and Experiment
• On the $Z_2$ classification of Quantum Spin Hall Models
• A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator
• Spin Charge Separation in the Quantum Spin Hall State
• Symmetry-protected topological phases and orbifolds: Generalized Laughlin's argument
• Conformal Field Theory of Composite Fermions

Cited by in corpus (16)

• Classification of topological quantum matter with symmetries
• On the coupling of Galilean-invariant field theories to curved spacetime
• Bulk-boundary correspondence in (3+1)-dimensional topological phases
• Global anomalies on the surface of fermionic symmetry-protected topological phases in (3+1) dimensions
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Conflicting Symmetries in Topologically Ordered Surface States of Three-dimensional Bosonic Symmetry Protected Topological Phases
• Topological Phases Protected By Reflection Symmetry and Cross-cap States
• ${\mathbb{Z}}_2$ fractional topological insulators in two dimensions
• Relationship between Symmetry Protected Topological Phases and Boundary Conformal Field Theories via the Entanglement Spectrum
• Global phase diagram of two-component Bose gases in antiparallel magnetic fields
• Three-dimensional Topological Insulators and Bosonization
• Coupled Wire Models of Interacting Dirac Nodal Superconductors
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Stability of Topological Insulators with Non-Abelian Edge Excitations
• Modular Anomalies in (2+1) and (3+1)-D Edge Theories