Nonperturbative Semiclassical Spin Dynamics for Ordered Quantum Magnets

Abstract

In ordered quantum magnets where interactions between elementary excitations dominate over their kinetic energy, perturbative approaches often fail, making non-perturbative methods essential to capture spectral features such as bound states and the redistribution of weight within excitation continua. Although an increasing number of experiments report anomalous spin excitation continua in such systems, their microscopic interpretation remains an open challenge. Here, we investigate the spin dynamics of the triangular-lattice antiferromagnet in its 1/3-plateau phase using two complementary non-perturbative approaches: exact diagonalization in a truncated Hilbert space for a gas of elementary excitations (THED) and matrix product state (MPS) simulations. Alongside cross-validation between these methods, we benchmark our results against inelastic neutron scattering (INS) data. The THED analysis confirms the presence of two-magnon bound states and identifies the anomalous scattering continuum observed in both MPS and INS as a two-magnon resonance, arising from hybridization between the bound state and the two-magnon continuum. Furthermore, THED reveals bound states overlapping with the continuum, enriching the interpretation of continuum anomalies. More broadly, THED provides a robust framework for investigating anomalous spin excitation continua and bound-state effects in other materials with gapped spectra. Its combination of accuracy and computational efficiency makes it a powerful tool for extracting reliable microscopic models in semiclassical regimes.

Figures (5)

• Figure 1: The 1/3 plateau phase of the TLAFM. a The up-up-down (UUD) magnetic order represented by red for spin-up and blue for spin-down states. b The magnetization curve of $\mathrm{KYbSe_2}$ under an external magnetic field, highlighting the 1/3 plateau. c The Brillouin zone of the triangular lattice (light blue shading) and the reduced Brillouin zone corresponding to the UUD order (light red shading), along with the chosen path. d Comparison of neutron scattering intensities for $\mathrm{KYbSe_2}$ at $B=4\ \mathrm{T}$ (marked by a star in panel b) with simulated results from the truncated Hilbert space exact diagonalization (THED) method and the time evolution of the matrix product state (MPS).
• Figure 2: Excitations of the classical Ising model up to two spin flips.a-- d Red (blue) circles represent spin-up (spin-down) states, while the orange dashed circle highlights the position of a spin flip. The energy cost associated with each excitation is shown above each panel.
• Figure 3: Schematic evolution of the two-magnon spectrum as a function of exchange anisotropy $\Delta$. The color indicates the quantum number $\Delta S^z$ of the corresponding state. Shaded regions represent the two-magnon continua. For $\Delta S^z=0$, solid lines denote two-magnon bound states, while dotted lines indicate two-magnon resonances. Dashed lines represent quadrupolar bound states with $\Delta S^z=-2$. The arrows indicate the lower and upper bounds of the overlapping continua.
• Figure 4: The two-magnon spectrum and the longitudinal dynamical spin structure factor $\mathcal{S}^{zz}(\bm{q},\omega)$ for different exchange anisotropies along the $(H,H,0)$ path.a-- c Two-magnon eigenvalues and quantum numbers $\Delta S^z$ obtained from the truncated Hilbert space exact diagonalization (THED) method for $\Delta = 5, 2$ and 1, respectively. d-- f Comparison of $\mathcal{S}^{zz}(\bm{q},\omega)$ for the same values of $\Delta = 5, 2$, and 1, as computing using THED and the time evolution of the matrix product state (MPS).
• Figure 5: Additional experimental verificationsa, b, c Comparison of the longitudinal dynamical spin structure factor $\mathcal{S}^{xx}(\bm{q},\omega)$ for $\mathrm{CsYbSe_2}$ at $B=4 \ T$ in the UUD phase obtained from INS, THED, and MPS. d, e, f Comparison of the INS intensities for $\mathrm{K_2Co(SeO_3)_2}$ with simulated results from THED and MPS.