Bridging entanglement dynamics and chaos in semiclassical systems

Abstract

It is widely recognized that entanglement generation and dynamical chaos are intimately related in semiclassical models. In this work, we propose a unifying framework which directly connects the bipartite and multipartite entanglement growth to the quantifiers of classical and quantum chaos. In the semiclassical regime, the dynamics of the von Neumann entanglement entropy, the spin squeezing, the quantum Fisher information and the out-of-time-order square commutator are governed by the divergence of nearby phase-space trajectories via the local Lyapunov spectrum, as suggested by previous conjectures in the literature. Analytical predictions are confirmed by detailed numerical calculations for two paradigmatic models, relevant in atomic and optical experiments, which exhibit a regular-to-chaotic transition: the quantum kicked top and the Dicke model.

Entanglement formation in continuous-variable random quantum networks

“…In this sense, the entanglement growth dynamics can be connected to projected phasespace volume growth (also see Ref. [71]), and it is clear that any choices of entanglement entropy will have similar dynamics.…”

Symmetries and conserved quantities of boundary time crystals in generalized spin models

“…BTCs have been first introduced in the context of fully connected spin models, where permutational invariance [42][43][44] allows the exact numerics up to rather large systems [45][46][47][48][49][50][51][52][53] and makes the mean-field description particularly reliable [42,[54][55][56][57][58]. In contrast to discrete time crystals, however, little is still understood about the conditions needed for the emergence of the BTC phase.…”

Measurement-induced criticality in (2+1)-d hybrid quantum circuits

“…Following a global quench starting from a generic low-entanglement (area-law) state, the von Neumann entropy of a given connected spatial partition grows linearly with time and relaxes to a value proportional to the partition volume (volume-law). Apart from remarkable exceptions, such as disorder-induced localized phases 5,6 , constrained quantum systems [7][8][9][10][11] and long-range models [12][13][14][15][16][17] , this trend is ubiquitous, as broadly documented by a wealth of theoretical studies [18][19][20][21][22][23][24][25][26] . Thanks to conceptual and technological advances in cold atom and trapped ions systems, Rényi entanglement entropies of moderately large partitions are nowadays experimentally measurable [27][28][29][30][31] .…”