Real-time dynamics of the subdiffusive random-field Heisenberg chain

We investigate the dynamics of an ergodic random-field Heisenerg chain near the diffusive-subdiffusive transition. Previous work (Znidaric, Scardicchio, and Varma, PRL 117, 040601) has found subdiffusive conductivity in numerical experiments on non-equilibrium steady states. We use the matrix product density operator technique DMT to simulate the real-time evolution of long ($L \gtrsim 256$ sites) spin-1/2 chains; we measure not only global dynamical exponents consistent with the results of Znidaric, Scardicchio, and Varma, but also the spatial variation of these exponents.