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arXiv · 2207.08353

R\'{e}nyi entanglement entropy after a quantum quench starting from insulating states in a free boson system

Daichi Kagamihara·Ryui Kaneko·Shion Yamashika·Kota Sugiyama·Ryosuke Yoshii·Shunji Tsuchiya·Ippei Danshita
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Abstract

We investigate the time-dependent R\'{e}nyi entanglement entropy after a quantum quench starting from the Mott-insulating and charge-density-wave states in a one-dimensional free boson system. The second R\'{e}nyi entanglement entropy is found to be the negative of the logarithm of the permanent of a matrix consisting of time-dependent single-particle correlation functions. From this relation and a permanent inequality, we obtain rigorous conditions for satisfying the volume-law entanglement growth. We also succeed in calculating the time evolution of the R\'{e}nyi entanglement entropy in unprecedentedly large systems by brute-force computations of the permanent. We discuss possible applications of our findings to the real-time dynamics of noninteracting bosonic systems.

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Daichi Kagamihara, Ryui Kaneko, Shion Yamashika, Kota Sugiyama, Ryosuke Yoshii, Shunji Tsuchiya, Ippei Danshita. 2022-07-18. R\'{e}nyi entanglement entropy after a quantum quench starting from insulating states in a free boson system. https://doi.org/10.1103/physreva.107.033305

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