An Interplay of Topology and Quantized Geometric Phase for two Different Symmetry-Class Hamiltonians

Abstract

Study of symmetry, topology and geometric phase can reveal many new and interesting results on the topological states of matter. Here we present a completely new and interesting result of symmetry, topology and quantization of geometric phase along with the physical explanation for two different symmetry classes. We present a detailed study of the auxiliary space for two different symmetry classes of Hamiltonians. We show explicitly that the origin of the auxiliary space inside the curve is only a necessary condition but it is not a sufficient condition for the topological state. One of the most interesting results is that same symmetry-class Hamiltonians show different behaviour in topology and quantized geometric phase.

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Cited by in corpus (3)

• Topological phase transition between non-high symmetry critical phases and curvature function renormalization group
• Extended edge modes and disorder preservation of a symmetry-protected topological phase out of equilibrium
• A Study of Curvature Theory for Different Symmetry Classes of Hamiltonian