Multiscale excitations in the diluted two-dimensional S=1/2 Heisenberg antiferromagnet - Liuyun Dao; Hui Shao; Anders W. Sandvik (Physical Review Research)
We study the excitation spectrum of the S=1/2 Heisenberg model on the randomly diluted square lattice by stochastic analytic continuation of imaginary-time correlations obtained by quantum Monte Carlo simulations in the low-temperature limit. Focusing on relatively low dilution fractions, p=1/16 and p=1/8, the dynamic structure factor S(q,ω) exhibits a strongly damped magnon peak with anomalous dispersion near q=(0,0) and (π,π), a nondispersive low-energy peak from localized excitations, and a second peak within the continuum connecting these two features. A magnon with anomalous logarithmic dispersion, close to our result, was predicted in spin wave and T-matrix theory [Chernyshev et al., Phys. Rev. B 65, 104407 (2002)0163-182910.1103/PhysRevB.65.104407], with the quasiparticle description breaking down at the low localization energy. However, no intermediate mode was predicted. Analyzing spectral functions in real space for individual vacancy realizations by energy tomography, we find that these excitations are concentrated on a subset of the spins adjacent to vacancies, with fewer spins involved as the energy is lowered. We argue that the low-energy excitations are those of a sparse random network of effective moments at a fraction of the vacancies, leading to a damped diffusive-like behavior with localization at the lowest energies (the localized mode). In the case of the magnon, there is a shift in the real-space spectral weight distribution, from the spins away from vacancies at high energy to those adjacent to vacancies at lower energy. We also analyze the Anderson quantum rotor excitation at ω∝N^{−1} (with N=L^{2} the system size), which in the clean system is visible in S(q,ω) only at q=(π,π) but spreads through the entire Brillouin zone due to the lack of translational invariance when p>0. Beyond weight close to q=(0,0) and (π,π), which we explain by local sublattice imbalance within a classical dimer-monomer model, there is also intricate structure arising from correlated singlet fluctuations, which we demonstrate by enhancing said fluctuations with four-spin couplings in the Hamiltonian. The features in momentum space reflect spatially nonuniform breaking of the spin rotation symmetry and should be experimentally observable with elastic neutron scattering on layered quantum antiferromagnets doped with nonmagnetic impurities. All the ω>0 excitations should be observable by inelastic neutron scattering. Technically, our work demonstrates that surprisingly complex spectral information can be obtained from quantum Monte Carlo data, despite the “ill-posed” numerical analytic continuation problem.