Flat-band ferrimagnetism in the edge-centered honeycomb antiferromagnet: From harmonic flat magnon to broad continuum
One of the most striking aspects of a flat band is not merely its lack of dispersion, but that it reduces the single-particle kinetic energy to a very small scale, allowing interaction effects to become the dominant energy scale in the low-energy physics. This picture has underpinned concepts such as flat-band ferromagnetism, flat-band superconductivity, and localized magnons. A more fundamental question, however, remains. Flat bands belong to the language of single-particle or linear-spin-wave physics; whether they survive as protected sharp excitations in a genuine many-body quantum magnet, or merely provide a skeleton of spectral weight left by the noninteracting picture, remains unclear. We study the spin-1/2 Heisenberg antiferromagnet on the edge-centered honeycomb lattice to examine this question. In contrast to flat bands in geometrically frustrated magnets such as kagome, this lattice has a 2:3 sublattice imbalance that renders the intersublattice coupling matrix rectangular, whose null space gives rise to a flat band at the single-particle level. The same imbalance stabilizes a ferrimagnetic ground state through the Lieb--Mattis theorem and leads to an edge-site-localized flat magnon in linear spin-wave theory. Combining linear spin-wave theory, sign-problem-free stochastic series expansion quantum Monte Carlo, and stochastic analytic continuation, we find that quantum fluctuations transform this harmonic flat mode into a broad continuum whose centroid is about 1.55J and nearly dispersionless along the high-symmetry path. Sublattice imbalance thus offers an unfrustrated route that unifies flat bands and ferrimagnetism, and suggests that flat-band geometry organizes many-body spectral weight rather than giving rise to a protected quasiparticle.