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• W2778488047 abstract "We study the distance of two wave functions under chaotic time evolution. The two initial states are differed only by a local perturbation. To be entitled chaos the distance should have a rapid growth afterwards. Instead of focusing on the entire wave function, we measure the distance $d^2(t)$ by investigating the difference of two reduced density matrices of the subsystem $A$ that is spatially separated from the local perturbation. This distance $d^2(t)$ grows with time and eventually saturates to a small constant. We interpret the distance growth in terms of operator scrambling picture, which relates $d^2(t)$ to the square of commutator $C(t)$ (out-of-time-order correlator) and shows that both these quantities measure the area of the operator wave front in subsystem $A$. Among various one-dimensional spin-$frac{1}{2}$ models, we numerically show that the models with non-local power-law interaction can have an exponentially growing regime in $d^2(t)$ when the local perturbation and subsystem $A$ are well separated. This regime is absent in the spin-$frac{1}{2}$ chain with local interaction only. After sufficiently long time evolution, $d^2(t)$ relaxes to a small constant, which decays exponentially as we increase the system size and is consistent with eigenstate thermalization hypothesis. Based on these results, we demonstrate that $d^2(t)$ is a useful quantity to characterize both quantum chaos and quantum thermalization in many-body wave functions." @default.
• W2778488047 created "2018-01-05" @default.
• W2778488047 creator A5004049354 @default.
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• W2778488047 date "2018-07-10" @default.
• W2778488047 modified "2023-09-24" @default.
• W2778488047 title "Measuring the distance between quantum many-body wave functions" @default.
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• W2778488047 doi "https://doi.org/10.1088/1742-5468/aace1f" @default.
• W2778488047 hasPublicationYear "2018" @default.
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