Magnetization and energy dynamics in spin ladders: Evidence of diffusion in time, frequency, position, and momentum

The dynamics of magnetization and energy densities are studied in the two-leg spin-1/2 ladder. Using an efficient pure-state approach based on the concept of typicality, we calculate spatiotemporal correlation functions for large systems with up to 40 lattice sites. In addition, two subsequent Fourier transforms from real to momentum space as well as from the time to frequency domain yield the respective dynamical structure factors. Summarizing our main results, we unveil the existence of genuine diffusion for both spin and energy. In particular, this finding is based on four distinct signatures which can all be equally well detected: (i) Gaussian density profiles, (ii) time-independent diffusion coefficients, (iii) exponentially decaying density modes, and (iv) Lorentzian line shapes of the dynamical structure factor. The combination of (i)-(iv) provides a comprehensive picture of high-temperature dynamics in this archetypal nonintegrable quantum model.