Energy diffusion in the ergodic phase of a many body localizable spin chain

Abstract

The phenomenon of many-body localization in disordered quantum many-body\nsystems occurs when all transport is suppressed despite the fact that the\nexcitations of the system interact. In this work we report on the numerical\nsimulation of autonomous quantum dynamics for disordered Heisenberg chains when\nthe system is prepared with an initial inhomogeneity in the energy density\nprofile. Using exact diagonalisation and a dynamical code based on Krylov\nsubspaces we are able to simulate dynamics for up to L = 26 spins. We find,\nsurprisingly, the breakdown of energy diffusion even before the many-body\nlocalization transition whilst the system is still in the ergodic phase.\nMoreover, in the ergodic phase we also find a large region in parameter space\nwhere the energy dynamics remains diffusive but where spin transport has been\npreviously evidenced to occur only subdiffusively: this is found to be true for\ninitial states composed of infinitely many hydrodynamic modes (square-wave\nenergy profile) or just the single longest mode (sinusoidal profile). This\nsuggestive finding points towards a peculiar ergodic phase where particles are\ntransported slower than energy, reminiscent of the situation in amorphous\nsolids and of the gapped phase of the anisotropic Heisenberg model.\n