Quasiparticle dynamics of symmetry resolved entanglement after a quench: the examples of conformal field theories and free fermions

Abstract

The time evolution of the entanglement entropy is a key concept to understand the structure of a non-equilibrium quantum state. In a large class of models, such evolution can be understood in terms of a semiclassical picture of moving quasiparticles spreading the entanglement throughout the system. However, it is not yet known how the entanglement splits between the sectors of an internal local symmetry of a quantum many-body system. Here, guided by the examples of conformal field theories and free-fermion chains, we show that the quasiparticle picture can be adapted to this goal, leading to a general conjecture for the charged entropies whose Fourier transform gives the desired symmetry resolved entanglement $S_n(q)$. We point out two physically relevant effects that should be easily observed in atomic experiments: a delay time for the onset of $S_n(q)$ which grows linearly with $|\hat{I}”q|$ (the difference from the charge $q$ and its mean value), and an effective equipartition when $|\hat{I}”q|$ is much smaller than the subsystem size.

7 pages, 2 figures