Forward approximation as a mean-field approximation for the Anderson and many-body localization transitions

@article{Pietracaprina2016ForwardAA,
  title={Forward approximation as a mean-field approximation for the Anderson and many-body localization transitions},
  author={Francesca Pietracaprina and Valentina Ros and Antonello Scardicchio},
  journal={Physical Review B},
  year={2016},
  volume={93},
  pages={054201}
}
In this paper we analyze the predictions of the forward approximation in some models which exhibit an Anderson (single-body) or many-body localized phase. This approximation, which consists of summing over the amplitudes of only the shortest paths in the locator expansion, is known to overestimate the critical value of the disorder which determines the onset of the localized phase. Nevertheless, the results provided by the approximation become more and more accurate as the local coordination… 
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