Abstract
We study and present the results of curvature for different symmetry classes (BDI, AIII and A) of model Hamiltonians and also present the transformation of model Hamiltonian from one distinct symmetry class to the other based on the curvature property. We observe the mirror symmetric curvature for the Hamiltonian with BDI symmetry class but there is no evidence of such behaviour for Hamiltonians of AIII symmetry class. We show the origin of torsion and its consequences on the parameter space of topological phase of the system. We find the evidence of torsion for the Hamiltonian of A symmetry class. We present Serret–Frenet equations for all model Hamiltonians in \(\mathbf {R}^3\) space. To the best of our knowledge, this is the first application of curvature theory to the model Hamiltonian of different symmetry classes which belong to the topological state of matter.
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Acknowledgements
SS would like to acknowledge DST (EMR/2017/ 000898) for the funding and RRI library for the books and journals. YRK would like to thank Admar Mutt Education Foundation for the scholarship. The authors would like to acknowledge Dr R Srikanth, Dr B S Ramachandra and Prof. C Sivaram for reading this manuscript critically and for giving useful suggestions. This research was supported in part by the International Centre for Theoretical Sciences (ICTS) during a visit for participating in the program – Geometry and Topology for Lecturers (Code: ICTS/gtl2018/06).
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Kartik, Y.R., Kumar, R.R., Rahul, S. et al. A study of curvature theory for different symmetry classes of Hamiltonian. Pramana - J Phys 95, 102 (2021). https://doi.org/10.1007/s12043-021-02134-9
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DOI: https://doi.org/10.1007/s12043-021-02134-9