Spin-resolved flat bands in a magnetized Lieb lattice are simply the zero-field bands shifted by ±Bz, because the Hamiltonian is block diagonal in spin.
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Magnetic Field Induced Band Deformation in a Lieb Lattice:Aharonov-Bohm Caging and Zeeman Splitting
Spin-resolved flat bands in a magnetized Lieb lattice are simply the zero-field bands shifted by ±Bz, because the Hamiltonian is block diagonal in spin.