Logarithmic entanglement growth and its fragility in systems of trapped spinless fermions

We consider a system of spinless fermions in a strong optical lattice plus a harmonic trap and
uncorrelated disorder. At a given time, we subject them to a quantum quench that consists of an instantaneous displacement of the trap centre - a plausible situation to realise in a cold-atom system.

In [1] we presented an analysis of the behaviour of the non-interacting version of the problem. We observe that (a) even weak disorder strongly breaks the parity symmetry of the clean problem, qualitatively changing the nature of the infinite-time steady state, and (b) the approach to this long-time state is extremely slow, since it involves the fermions' tunnelling across a broad 'Bragg-forbidden' region.
Here we show that the ingredients in the above study also present a way to realise slow logarithmic entanglement growth as usually observed in many-body localized systems without disorder or even without interactions. We present evidence for this by a time-evolving block decimation and exact diagonalization analysis of the interacting and non-interacting case.

[1] M. Schulz, C.A. Hooley and R. Moessner, Phys. Rev. A. 94, 063643 (2016).