Decoherence-independent transport in the Harper-Hofstadter-Aubry-André model at criticality.

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

Santiago de Chile

Workshop; Conference and Advanced School on Low-Dimensional Quantum Systems | (smr 3820); 2023

ICTP

While static disorder can induce a Metal-Insulator Transition (MIT) into a localized regime, time-dependent noise or local interactions with a reservoir may destroy this local-lization and cause diffusion[1]. Conversely, in the ballistic regime, decoherence limits the perfect transport. However, how the competence between noise and disorder manifests on transport properties at the MIT is still an open question. We investigate this question in a paradigmatic system with a MIT, the Harper-Hofstadter-Aubry-Andr ́e (HHAA) 1D model[2, 3], 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 diffusively. There, a regime of decoherent-independent transport arises, characterized by an intrinsic diffusion coefficient until the coherence time becomes comparable with the time between elastic collisions. We also investigate the decay of the purity or Loschmidt echo, a usual quantifier of coherence. The long time decay is determined only by the diffusion coefficient and thus, it is independent of the decoherence rate.A supplementary analysis was carried out for other models whose quantum dynam-cs can show excitation spreading that assimilates to diffusion (Fibonacci chain and the Power-Banded random matrices (PBRM)[4]), finding the same  behavior. This paves the way to understand the role of MIT and diffusion in the stabilization of the transport properties under external perturbations.[1] H. M. Pastawski. Phys. Rev. B 44.12 (1991): 6329.[2] Sokoloff, J. B. Phys. Rep. 126.4 (1985): 189-244.[3] F. S. Lozano-Negro, et al. Chaos Solit. Fractals 150 (2021): 111175.[4] N. Calderon Chavez, G. L. Celardo. BUAP. PhD Thesis (2020).