Fractional corner magnetization of collinear antiferromagnets

Abstract

Recent studies revealed that the electric multipole moments of insulators result in fractional electric charges localized to the hinges and corners of the sample. We here explore the magnetic analog of this relation. We show that a collinear antiferromagnet with spin S defined on a ddimensional cubic lattice features fractionally quantized magnetization M z c = S/2 d at the corners. We find that the quantization is robust even in the presence of gapless excitations originating from the spontaneous formation of the Néel order, although the localization length diverges, suggesting a power-law localization of the corner magnetization. When the spin rotational symmetry about the z axis is explicitly broken, the corner magnetization is no longer sharply quantized. Even in this case, we numerically find that the deviation from the quantized value is negligibly small based on quantum Monte Carlo simulations.

Higher-order topology and corner triplon excitations in two-dimensional quantum spin-dimer models

“…In addition to these platforms, proposals to observe HOT physics in quantum spin systems [14][15][16] and solvable spin liquid models [17][18][19] have also been put forward. While investigations of HOT phases in these spin systems have mainly focused on ground-state physics, their generalization to excited states is relatively less explored.…”