An index theorem for quarter-plane Toeplitz operators via extended symbols and gapped invariants related to corner states

DOI10.1007/s00220-022-04600-wzbMath1525.47059arXiv2203.09117OpenAlexW4225700514MaRDI QIDQ6038761

Shin Hayashi

Publication date: 3 May 2023

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.09117

zbMATH Keywords

topological invariantsToeplitz operatorsFredholm indicesmatrix factorisationsbulk Hamiltonians

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) (Semi-) Fredholm operators; index theories (47A53) Many-body theory; quantum Hall effect (81V70)

Cites Work

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• Bulk and boundary invariants for complex topological insulators. From \(K\)-theory to physics
• \(K\)-theory for real \(C^*\)-algebras via unitary elements with symmetries
• Twisted equivariant matter
• Bulk-edge correspondence for two-dimensional topological insulators
• Transformation groups
• Topological methods for C*-algebras. II: Geometric resolutions and the Kuenneth formula
• Factorization of matrix functions and singular integral operators
• Topological invariants and corner states for Hamiltonians on a three-dimensional lattice
• Classification of topological invariants related to corner states
• Toeplitz operators on concave corners and topologically protected corner states
• Equivariant cohomology theories
• Banach algebras and Bott periodicity
• The index of elliptic operators. III
• Index theory for skew-adjoint Fredholm operators
• An index theorem for Wiener-Hopf operators on the discrete quarter-plane
• Convex Structures and Continuous Selections
• Periodic table for topological insulators and superconductors
• The noncommutative geometry of the quantum Hall effect
• EDGE CURRENT CHANNELS AND CHERN NUMBERS IN THE INTEGER QUANTUM HALL EFFECT
• Chern number and edge states in the integer quantum Hall effect
• Quantized electric multipole insulators
• Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter
• K-THEORY AND REALITY
• BOTT PERIODICITY AND THE INDEX OF ELLIPTIC OPERATORS
• FACTORIZATION OF PARAMETER-DEPENDENT MATRIX-FUNCTIONS IN NORMED RINGS AND CERTAIN RELATED QUESTIONS IN THE THEORY OF NOETHERIAN OPERATORS
• On the C ∗ -Algebra of Toeplitz Operators on the Quarter-Plane