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arXiv · 1908.02773

Locality and Heating in Periodically Driven, Power-law Interacting Systems

Minh C. Tran·Adam Ehrenberg·Andrew Y. Guo·Paraj Titum·Dmitry A. Abanin·Alexey V. Gorshkov
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Abstract

We study the heating time in periodically driven $D$-dimensional systems with interactions that decay with the distance $r$ as a power-law $1/r^\alpha$. Using linear response theory, we show that the heating time is exponentially long as a function of the drive frequency for $\alpha>D$. For systems that may not obey linear response theory, we use a more general Magnus-like expansion to show the existence of quasi-conserved observables, which imply exponentially long heating time, for $\alpha>2D$. We also generalize a number of recent state-of-the-art Lieb-Robinson bounds for power-law systems from two-body interactions to $k$-body interactions and thereby obtain a longer heating time than previously established in the literature. Additionally, we conjecture that the gap between the results from the linear response theory and the Magnus-like expansion does not have physical implications, but is, rather, due to the lack of tight Lieb-Robinson bounds for power-law interactions. We show that the gap vanishes in the presence of a hypothetical, tight bound.

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Minh C. Tran, Adam Ehrenberg, Andrew Y. Guo, Paraj Titum, Dmitry A. Abanin, Alexey V. Gorshkov. 2019-08-07. Locality and Heating in Periodically Driven, Power-law Interacting Systems. https://doi.org/10.1103/physreva.100.052103

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