Dephasing independent transport in the diffusive coherent regime around criticality.

FABRICIO S. LOZANO N.; PASTAWSKI, HORACIO M.; FAUSTO BORGONOVI; GIUSEPPE LUCA CELARDO

Cordoba

Congreso; QUATOS 5; 2023

While on-site static disorder in a crystal can induce a Metal-Insulator Transition (MIT) into a localized regime, a local time-dependent noise or interactions with an environment may induce decoherence that destroys this localization and enable diffusion. Conversely, in the ballistic regime, decoherence limits the perfect transport. However, the details of how noise and disorder compete to yield the transport properties at the MIT is still an open question. We investigate this question in a paradigmatic system, the Harper-Hofstadter-Aubry-André (HHAA) 1D model, in the presence of a decoherent environment.  We show that at the MIT the elastic collisions induce a quantum dynamics where a local excitation spreads with an intrinsic diffusion coefficient. This spreading remains decoherent-independent until the coherence time becomes comparable with the time between elastic collisions. In this model of local decoherence, the long time decay of the purity or Loschmidt echo is determined only by the diffusion coefficient and thus, it is also  independent of the decoherence rate. A supplementary analysis was  carried out for two other models whose quantum excitation spreading  could be assimilated to diffusion (Fibonacci chain and the Power-Banded  Random Matrices (PBRM)), finding the decoherence-independent  transport regime. This paves the way to understand the role of MIT and  diffusion in the stabilization of the transport properties under external  perturbations.