Entanglement revivals as a probe of scrambling in finite quantum systems

Abstract

The entanglement evolution after a quantum quench became one of the tools to distinguish integrable versus chaotic (non-integrable) quantum many-body dynamics. Following this line of thoughts, here we propose that the revivals in the entanglement entropy provide a finite-size diagnostic benchmark for the purpose. Indeed, integrable models display periodic revivals manifested in a dip in the block entanglement entropy in a finite system. On the other hand, in chaotic systems, initial correlations get dispersed in the global degrees of freedom (information scrambling) and such a dip is suppressed. We show that while for integrable systems the height of the dip of the entanglement of an interval of fixed length decays as a power law with the total system size, upon breaking integrability a much faster decay is observed, signalling strong scrambling. Our results are checked by exact numerical techniques in free-fermion and free-boson theories, and by time-dependent density matrix renormalisation group in interacting integrable and chaotic models.

Entanglement spreading in non-equilibrium integrable systems

“…(44) is washed out [226]. In full analogy with the mutual information, the disappearance of such dip is a quantitive measure of scrambling [205].…”

“…where {x} denotes the fractional part of x, e.g., {7.36} = 0.36. This form has been carefully tested for free systems [205] in which it is possible to handle very large sizes. For interacting models, tensor network simulations work well only for relatively small values of L, but still the agreement is satisfactory [205].…”

“…Although the prediction for the entanglement entropy of a single interval in an infinite system is the same for both the quasiparticle and the minimal membrane pictures, the two rely on very different physical mechanisms and should provide different results for other entanglement related quantities. In fact, it has been found that the behaviour of the entanglement of disjoint regions [222][223][224][225] or that of one interval in finite volume [205,219,220,226] is qualitatively different. For maximally chaotic systems, the mutual information and the negativity of disjoint intervals are constantly zero and do not exhibit the peak from the quasiparticle picture seen in Eq.…”

Prethermalization and thermalization in entanglement dynamics

“…The two pictures discussed above rely on very different physical mechanisms and in general give different predictions. For instance, their predictions for the dynamics of the entanglement of disjoint regions [12,21] or that of a connected region in finite volume [22,51,72] are qualitatively different. In essence, while correlated quasiparticles produce disentanglement whenever the pairs find themselves in the same subsystem in the course of the evolution, no disentanglement is observed in the nonintegrable case.…”

“…The non-equilibrium dynamics of the entanglement in many-body systems is currently attracting huge attention, effectively bridging the gap between condensed matter, quantum information, and high-energy physics. Some of the big questions in this context concern the onset of thermalisation in isolated many-body systems [1][2][3][4], the origin of thermodynamic entropy [5][6][7][8][9][10][11], the scrambling of quantum information in quantum chaotic systems [12][13][14][15][16][17][18][19][20][21][22], as well as the simulability of the quantum many-body dynamics via classical computers [23][24][25][26][27].…”