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arXiv · 1705.06171

Zeros of Loschmidt echo in the presence of Anderson localization

Honghao Yin·Shu Chen·Gao Xianlong·Pei Wang
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Abstract

We study the Loschmidt echo and the dynamical free energy of the Anderson model after a quench of the disorder strength. If the initial state is extended and the eigenstates of the post-quench Hamiltonian are strongly localized, we argue that the Loschmidt echo exhibits zeros periodically with the period $2\pi /D$ where $D$ is the width of spectra. At these zeros, the dynamical free energy diverges in a logarithmic way. We present numerical evidence of our argument in one- and three-dimensional Anderson models. Our findings connect the dynamical quantum phase transitions to the localization-delocalization phase transitions.

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Honghao Yin, Shu Chen, Gao Xianlong, Pei Wang. 2017-05-17. Zeros of Loschmidt echo in the presence of Anderson localization. https://doi.org/10.1103/physreva.97.033624

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