Halperin (m',m,n) Fractional Quantum Hall Effect in Topological Flat Bands

The Halperin (m',m,n) fractional quantum Hall effects of two-component quantum particles are studied in topological checkerboard lattice models. Here for m≠ m', we demonstrate the emergence of fractional quantum hall effects with the associated 𝐊=[ m+2 1; 1 m; ] matrix (even m=2 for boson and odd m=3 for fermion) in the presence of both strong intercomponent and intracomponent repulsions. Through exact diagonalization and density-matrix renormalization group calculations, we elucidate their topological fractionalizations, including (i) the |𝐊|=(m^2+2m-1)-fold ground-state degeneracies and (ii) fractionally quantized topological Chern number matrix 𝐂=𝐊^-1. Our flat band model provides a paradigmatic example of a microscopic Hamiltonian featuring fractional quantum Hall effect with partial spin-polarization.