Universal robustness to decoherence in the quantum diffusive regime

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

Trieste

Workshop; School on Quantum Many-Body Phenomena out of Equilibrium: from Chaos to Criticality | (smr 3867); 2023

ICTP

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 any environment may induce decoherence that destroys this localization and enables 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 by using a paradigmatic 1D system, the Harper-Hofstadter-Aubry-Andre (HHAA) model, in the presence of a decoherent environment. We show that, at the MIT, a local quantum excitation spreads with an intrinsic diffusion coefficient which remains essentially decoherence-independent until the decoherence time becomes comparable with a time that characterizes the elastic collisions. In this model of local decoherence, thelong 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. In order to determine if this is a property of the MIT or a characteristic of quantum diffusion, a supplementary analysis was carried out for two other models whose quantum excitation spreading could be assimilated to diffusion, the Fibonacci chain and the Power-Banded Random Matrices (PBRM), but only the last has a MIT. By rescaling the data we find the diffusion coefficient with the decoherence strength has a universal behavior. This paves the way to understand the crucial role of diffusion in the stabilization of the transport properties under external perturbations.