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Abstract
Topological spaces have numerous applications for quantum matter with protected chiral edge modes related to an integer-valued Chern number, which also characterizes the global response of a spin-1/2 particle to a magnetic field. Such spin-1/2 models can also describe topological Bloch bands in lattice Hamiltonians. Here we introduce interactions in a system of spin-1/2s to reveal a class of topological states with rational-valued Chern numbers for each spin providing a geometrical and physical interpretation related to curvatures and quantum entanglement. We study a driving protocol in time to reveal the stability of the fractional topological numbers towards various forms of interactions in the adiabatic limit. We elucidate a correspondence of a one-half topological spin response in bilayer semimetals on a honeycomb lattice with a nodal ring at one Dirac point and a robust π Berry phase at the other Dirac point.
Highlights
Topological spaces have numerous applications for quantum matter with protected chiral edge modes related to an integer-valued Chern number, which characterizes the global response of a spin-1/2 particle to a magnetic field
We show applications of the spheres with C 1⁄4 1=2 per spin for the characterization of topological semimetallic phases in bilayer honeycomb systems showing one Dirac point associated with a π Berry phase and another Dirac point revealing a nodal entangled ring
We have shown the stability of the fractional Chern number regarding various forms of interactions in the adiabatic limit
Summary
Topological spaces have numerous applications for quantum matter with protected chiral edge modes related to an integer-valued Chern number, which characterizes the global response of a spin-1/2 particle to a magnetic field. Equation (9) is an interesting generalization of Eq (1) because this shows that one can yet define and measure for these interacting models in curved space the topology from the magnetizations of a given spin j at the poles.
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