@article{834,
  abstract     = {Thermal and many-body localized phases are separated by a dynamical phase transition of a new kind. We analyze the distribution of off-diagonal matrix elements of local operators across this transition in two different models of disordered spin chains. We show that the behavior of matrix elements can be used to characterize the breakdown of thermalization and to extract the many-body Thouless energy. We find that upon increasing the disorder strength the system enters a critical region around the many-body localization transition. The properties of the system in this region are: (i) the Thouless energy becomes smaller than the level spacing, (ii) the matrix elements show critical dependence on the energy difference, and (iii) the matrix elements, viewed as amplitudes of a fictitious wave function, exhibit strong multifractality. This critical region decreases with the system size, which we interpret as evidence for a diverging correlation length at the many-body localization transition. Our findings show that the correlation length becomes larger than the accessible system sizes in a broad range of disorder strength values and shed light on the critical behavior near the many-body localization transition.},
  author       = {Serbyn, Maksym and Zlatko, Papic and Abanin, Dmitry},
  issn         = {24699950},
  journal      = {Physical Review B - Condensed Matter and Materials Physics},
  number       = {10},
  publisher    = {American Physical Society},
  title        = {{Thouless energy and multifractality across the many-body localization transition}},
  doi          = {10.1103/PhysRevB.96.104201},
  volume       = {96},
  year         = {2017},
}

@article{724,
  abstract     = {We investigate the stationary and dynamical behavior of an Anderson localized chain coupled to a single central bound state. Although this coupling partially dilutes the Anderson localized peaks towards nearly resonant sites, the most weight of the original peaks remains unchanged. This leads to multifractal wave functions with a frozen spectrum of fractal dimensions, which is characteristic for localized phases in models with power-law hopping. Using a perturbative approach we identify two different dynamical regimes. At weak couplings to the central site, the transport of particles and information is logarithmic in time, a feature usually attributed to many-body localization. We connect such transport to the persistence of the Poisson statistics of level spacings in parts of the spectrum. In contrast, at stronger couplings the level repulsion is established in the entire spectrum, the problem can be mapped to the Fano resonance, and the transport is ballistic.},
  author       = {Hetterich, Daniel and Serbyn, Maksym and Domínguez, Fernando and Pollmann, Frank and Trauzettel, Björn},
  issn         = {24699950},
  journal      = {Physical Review B},
  number       = {10},
  publisher    = {American Physical Society},
  title        = {{Noninteracting central site model localization and logarithmic entanglement growth}},
  doi          = {10.1103/PhysRevB.96.104203},
  volume       = {96},
  year         = {2017},
}