On the $C^*$-algebraic approach to topological phases for insulators

Autor: Johannes Kellendonk
Přispěvatelé: Institut Camille Jordan [Villeurbanne] ( ICJ ), École Centrale de Lyon ( ECL ), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Institut National des Sciences Appliquées de Lyon ( INSA Lyon ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Université Jean Monnet [Saint-Étienne] ( UJM ) -Centre National de la Recherche Scientifique ( CNRS ), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Probabilités, statistique, physique mathématique (PSPM), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL)
Jazyk: angličtina
Rok vydání: 2017
Předmět:
Nuclear and High Energy Physics
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]
FOS: Physical sciences
Insulator (electricity)
Topological space
Topology
01 natural sciences
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]
Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
0103 physical sciences
FOS: Mathematics
[ PHYS.PHYS.PHYS-GEN-PH ] Physics [physics]/Physics [physics]/General Physics [physics.gen-ph]
Topological insulators
0101 mathematics
Algebraic number
Mathematical Physics
Physics
19K99
Condensed Matter - Mesoscale and Nanoscale Physics
Homotopy
010102 general mathematics
K-Theory and Homology (math.KT)
Statistical and Nonlinear Physics
Observable
Mathematical Physics (math-ph)
[PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph]
Homogeneous space
Mathematics - K-Theory and Homology
[ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph]
010307 mathematical physics
Zdroj: Annales Henri Poincare
Annales Henri Poincare, 2017, 18 (7), pp.2251-2300. 〈10.1007/s00023-017-0583-0〉
Annales Henri Poincare, 2017, 18 (7), pp.2251-2300. ⟨10.1007/s00023-017-0583-0⟩
Annales Henri Poincaré
Annales Henri Poincaré, Springer Verlag, 2017, 18 (7), pp.2251-2300. ⟨10.1007/s00023-017-0583-0⟩
ISSN: 1424-0637
1424-0661
DOI: 10.1007/s00023-017-0583-0〉
Popis: The notion of a topological phase of an insulator is based on the concept of homotopy between Hamiltonians. It therefore depends on the choice of a topological space to which the Hamiltonians belong. We advocate that this space should be the $C^*$-algebra of observables. We relate the symmetries of insulators to graded real structures on the observable algebra and classify the topological phases using van Daele's formulation of $K$-theory. This is related but not identical to Thiang's recent approach to classify topological phases by $K$-groups in Karoubi's formulation.
Version 2 accidentally merged with version 1. Major generalisation of discussion of real structures. Version 4: Revision and errors corrected
Databáze: OpenAIRE
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