Entanglement dynamics following a sudden quench: an exact solution

Abstract

We present an exact and fully analytical treatment of the entanglement dynamics for an isolated system of $N$ coupled oscillators following a sudden quench of the system parameters. The system is analyzed using the solutions of the time dependent Schrodinger's equation, which are obtained by solving the corresponding nonlinear Ermakov equations. The entanglement entropies exhibit a multi-oscillatory behaviour, where the number of dynamically generated time scales increases with $N$. The harmonic chains exhibit entanglement revival and for larger values of $N(>10)$, we find near-critical logarithmic scaling for the entanglement entropy, which is modulated by a time dependent factor. The $N=2$ case is equivalent to the two site Bose-Hubbard model in the tunneling regime, which is amenable to empirical realization in cold atom systems.

Figure for large N added, discussion related with near critical scaling behavior added

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• Dynamical scaling symmetry and asymptotic quantum correlations for time-dependent scalar fields
• Circuit Complexity in an interacting quenched Quantum Field Theory
• Entanglement in interacting quenched two-body coupled oscillator system
• Evolution of circuit complexity in a harmonic chain under multiple quenches
• Dynamics and Redistribution of Entanglement and Coherence in Three Time-Dependent Coupled Harmonic Oscillators
• Magnetic Field Effect on Dynamics of Entanglement for Time-dependent Harmonic Oscillator
• Evolution of capacity of entanglement and modular entropy in harmonic chains and scalar fields
• Time-dependent Hamiltonians and Geometry of Operators Generated by Them
• Quantum Quench in $c=1$ Matrix Model and Emergent Space-times
• Entanglement in a Maxwell Theory coupled to a non-relativistic particle