Many-body localization in the interpolating Aubry-André-Fibonacci model

We investigate the localization properties of a spin chain with an antiferromagnetic nearest-neighbor coupling,
subject to an external quasiperiodic on-site magnetic field. The quasiperiodic modulation interpolates between
two paradigmatic models, namely the Aubry-André and the Fibonacci models. We find that stronger many-
body interactions extend the ergodic phase in the former, whereas they shrink it in the latter. Furthermore,
the many-body localization transition points at the two limits of the interpolation appear to be continuously
connected along the deformation of the quasiperiodic modulation. As a result, the position of the many-body
localization transition depends on the interaction strength for an intermediate degree of deformation. Moreover,
in the region of parameter space where the single-particle spectrum contains both localized and extended states,
many-body interactions induce an anomalous effect: weak interactions localize the system, whereas stronger
interactions enhance ergodicity. We map the model’s localization phase diagram using the decay of the quenched
spin imbalance in relatively long chains. This is accomplished employing a time-dependent variational approach
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applied to a matrix product state decomposition of the many-body state. Our model serves as a rich playground
for testing many-body localization under tunable potential