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

• URL: http://arxiv.org/abs/2207.08353v2
• Date: Sat, 14 Jan 2023 05:37:42 GMT
• Title: R\'{e}nyi entanglement entropy after a quantum quench starting from insulating states in a free boson system
• Authors: Daichi Kagamihara, Ryui Kaneko, Shion Yamashika, Kota Sugiyama, Ryosuke Yoshii, Shunji Tsuchiya, Ippei Danshita
• Abstract summary: We investigate the time-dependent R'enyi entanglement entropy after a quantum quench. We calculate the time evolution of the R'enyi entanglement entropy in unprecedentedly large systems. We discuss possible applications of our findings to the real-time dynamics of noninteracting bosonic systems.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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