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Title:
Open quantum system generalization of Incommensurate lattice models in low dimensions
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Abstract:
We will discuss properties of incommensurate lattice models in low dimensions. In particular, in the well-known Aubry-Andre-Harper (AAH) model, an interesting sub-diffusive scaling of non-equilibrium steady state current with system size at critical point will be discussed. A novel approach will be introduced for probing the phase diagram by computing spatial profiles of experimentally accessible NESS quantities. A detailed study of certain closed system quantities was made such as wave-function spread, dynamical susceptibility and current auto-correlation functions and hints of anomalous transport was found but there was no clear evidence of sub-diffusion seen in the open system. A deformation of AAH (GAAH) which has a mobility edge was also investigated. Interesting phase diagram and a surprising and highly non-trivial correspondence between the eigenstates of GAAH model and those of AAH model were found. It was found that the co-existence of localized and delocalized phases in the presence of a mobility edge has a clear signature in the time evolution of particle density profiles, and this universal feature has recently been experimentally seen in a 1D model with mobility edge (by the experimental group of Immanuel Bloch).
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