Dynamic structure factor of the spin-12XXZ chain in a transverse field

The spin-$\frac{1}{2}$ XXZ chain with easy-plane anisotropy in a transverse field describes well the thermodynamic properties of the material ${\mathrm{Cs}}₂{\mathrm{CoCl}}₄$ in a wide range of temperatures and fields including the region close to the spin-flop Ising quantum phase transition. For a comparison with prospective inelastic neutron scattering experiments on this compound, we present results of an extensive numerical study of its dynamic structure factor ${\mathcal{S}}^{\ensuremath{\alpha}\ensuremath{\beta}}(k,\ensuremath{\omega})$ using matrix-product-state (MPS) techniques. Close to criticality, the dynamic part of the correlator ${\mathcal{S}}^xx$ longitudinal to the applied field is incoherent and possesses a small total weight as the ground state is already close to saturation. The transverse correlator ${\mathcal{S}}^zz$, on the other hand, is dominated by a coherent single-particle excitation with additional spectral weight at higher energies that we tentatively attribute to a repulsively bound pair of particles. With increasing temperature, the latter quickly fades and spectral weight instead accumulates close to zero wave vector just above the single-particle energy. On a technical level, we compare the numerical efficiency of real-time evolution to an MPS-based Chebyshev expansion in the present context, finding that both methods yield results of similar quality at comparable numerical costs.