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arXiv · 1703.07489

Dynamical signature of localization-delocalization transition in one-dimensional incommensurate lattice

Chao Yang·Yucheng Wang·Pei Wang·Gao Xianlong·Shu Chen
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Abstract

We investigate the quench dynamics of a one-dimensional incommensurate lattice described by the Aubry-André model by a sudden change of the strength of incommensurate potential $Δ$ and unveil that the dynamical signature of localization-delocalization transition can be characterized by the occurrence of zero points in the Loschmit echo. For the quench process with quenching taking place between two limits of $Δ=0$ and $Δ=\infty$, we give analytical expressions of the Loschmidt echo, which indicate the existence of a series of zero points in the Loschmidt echo. For a general quench process, we calculate the Loschmidt echo numerically and analyze its statistical behavior. Our results show that if both the initial and post-quench Hamiltonian are in extended phase or localized phase, Loschmidt echo will always be greater than a positive number; however if they locate in different phases, Loschmidt echo can reach nearby zero at some time intervals.

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Chao Yang, Yucheng Wang, Pei Wang, Gao Xianlong, Shu Chen. 2017-03-22. Dynamical signature of localization-delocalization transition in one-dimensional incommensurate lattice. https://doi.org/10.1103/physrevb.95.184201

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