Roton Minimum as a Fingerprint of Magnon-Higgs Scattering in Ordered Quantum Antiferromagnets

A quantitative description of magnons in long-range ordered quantum antiferromagnets is presented which is consistent from low to high energies. It is illustrated for the generic $S=1/2$ Heisenberg model on the square lattice. The approach is based on a continuous similarity transformation in momentum space using the scaling dimension as the truncation criterion. Evidence is found for significant magnon-magnon attraction inducing a Higgs resonance. The high-energy roton minimum in the magnon dispersion appears to be induced by strong magnon-Higgs scattering.

Figure 1

One-magnon dispersion $\omega (\mathbf{k})$ in the magnetic BZ. Circles depict CST data for $L=16$; diamonds, squares, and triangles show data from the spin-wave theory [15], series expansion, and QMC simulations extrapolated to the thermodynamic limit [17]. Inset: Extrapolation of the dispersion at momenta $(\pi ,0)$ and $(\pi /2,\pi /2)$ (circles). The squares depict the series expansion and the triangles up the QMC data [17].

Figure 2

Two-magnon part of the longitudinal dynamic structure factor $S^{zz}(\mathbf{k},\omega )$. Dotted black line, without interaction; dashed blue line, bare interaction; solid red line, renormalized interaction. The curves are computed for $L=192$ by using the matrix elements of the $L=16$ system and broadened by $0.013J$. The dispersion is interpolated smoothly, the interaction in a piecewise constant way.