کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1894781 1533752 2014 36 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Classification of “Real” Bloch-bundles: Topological quantum systems of type AI
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات فیزیک ریاضی
پیش نمایش صفحه اول مقاله
Classification of “Real” Bloch-bundles: Topological quantum systems of type AI
چکیده انگلیسی

We provide a classification of type AI topological quantum systems in dimension d=1,2,3,4d=1,2,3,4 which is based on the equivariant   homotopy properties of “Real” vector bundles. This allows us to produce a fine classification able to take care also of the non stable regime which is usually not accessible via KK-theoretic techniques. We prove the absence of non-trivial phases for one-band AI free or periodic quantum particle systems in each spatial dimension by inspecting the second equivariant cohomology group which classifies “Real” line bundles. We also show that the classification of “Real” line bundles suffices for the complete classification of AI topological quantum systems in dimension d⩽3d⩽3. In dimension d=4d=4 the determination of different topological phases (for free or periodic systems) is fixed by the second “Real” Chern class which provides an even labeling identifiable with the degree of a suitable map. Finally, we provide explicit realizations of non trivial 4-dimensional free models for each given topological degree.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 86, December 2014, Pages 303–338
نویسندگان
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