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- W4210724071 abstract "Abstract We consider quasifree ground states of Araki’s self-dual canonical anti-commutation relation algebra from the viewpoint of index theory and symmetry protected topological (SPT) phases. We first review how Clifford module indices characterise a topological obstruction to connect pairs of symmetric gapped ground states. This construction is then generalised to give invariants in <?CDATA $K{O}_{ast }({A}^{mathfrak{r}})$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll><mml:mi>K</mml:mi><mml:msub><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=fraktur>r</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:math> with A a <?CDATA ${C}^{ast ,mathfrak{r}}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo><mml:mo>,</mml:mo><mml:mi mathvariant=fraktur>r</mml:mi></mml:mrow></mml:msup></mml:math> -algebra of allowed deformations. When A = C *( X ), the Roe algebra of a coarse space X , and we restrict to gapped ground states that are locally equivalent with respect X , a K -homology class is also constructed. The coarse assembly map relates these two classes and clarifies the relevance of K -homology to free-fermionic SPT phases." @default.
- W4210724071 created "2022-02-08" @default.
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- W4210724071 date "2022-03-02" @default.
- W4210724071 modified "2023-10-12" @default.
- W4210724071 title "Locally equivalent quasifree states and index theory" @default.
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- W4210724071 doi "https://doi.org/10.1088/1751-8121/ac508b" @default.
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