Free fermions at the edge of interacting systems

@article{Stephan2019FreeFA,
  title={Free fermions at the edge of interacting systems},
  author={Jean-Marie St'ephan},
  journal={SciPost Physics},
  year={2019}
}
We study the edge behavior of inhomogeneous one-dimensional quantum systems, such as Lieb-Liniger models in traps or spin chains in spatially varying fields. For free systems these fall into several universality classes, the most generic one being governed by the Tracy-Widom distribution. We investigate in this paper the effect of interactions. Using semiclassical arguments, we show that since the density vanishes to leading order, the strong interactions in the bulk are renormalized to zero at… 

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