Dynamical properties of quantum many-body systems with long-range interactions

Employing large-scale quantum Monte Carlo simulations, we systematically compute the energy spectra of the two-dimensional (2D) spin-1/2 Heisenberg model with long-range interactions. With the 1/r & alpha; ferromagnetic and staggered antiferromagnetic interactions, we find the explicit range in & alpha; for the short-range Goldstone-type (gapless), anomalous Goldstone-type (gapless), and Higgs-type (gapped) spectra. Accompanied by the spin-wave analysis, our numerical results vividly reveal how the long-range interactions alter the usual linear and quadratic magnon dispersions in 2D quantum magnets and give rise to anomalous dynamical exponents. Moreover, we find the explicit case where the gapped excitation emerges at a noninteger decay exponent & alpha; for the antiferromagnetic Hamiltonian. This work provides the first set of unbiased dynamical data of long-range quantum many-body systems and suggests that many universally accepted low-energy customs for short-range systems need to be substantially modified for long-range ones, which are of immediate relevance to the ongoing experimental efforts from quantum simulators to 2D quantum moire materials.