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

TL;DR

This paper studies the evolution of Rényi entanglement entropy after a quantum quench in a free boson system, revealing a relation to matrix permanents and establishing conditions for volume-law growth.

Contribution

It introduces a novel relation between Rényi entropy and matrix permanents, enabling large-scale computations and rigorous conditions for entanglement growth in free bosonic systems.

Findings

Derived a relation between Rényi entropy and matrix permanents.

Established conditions for volume-law entanglement growth.

Successfully computed entanglement dynamics in large systems.

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.