Linear and logarithmic entanglement production in an interacting chaotic quantum system

Jayendra N. Bandyopadhyay, Arul Lakshminarayan

C. W. J. Beenakker, M. Kindermann, Charles M. Marcus +1 more

Sanku Paul, Arnd Bäcker

We investigate entanglement growth for a pair of coupled kicked rotors. For weak coupling, the growth of the entanglement entropy is found to be initially linear followed by a logarithmic growth. We calculate analytically the time after which the entanglement entropy changes its profile, and a good agreement with the numerical result is found. We further show that the different regimes of entanglement growth are associated with different rates of energy growth displayed by a rotor. At a large time, energy grows diffusively, which is preceded by an intermediate dynamical localization. The time span of intermediate dynamical localization decreases with increasing coupling strength. We argue that the observed diffusive energy growth is the result of one rotor acting as an environment to the other, which destroys the coherence. We show that the decay of the coherence is initially exponential followed by a power law.

Vincenzo Alba, Jérôme Dubail, Marko Medenjak

In a many-body quantum system, local operators in the Heisenberg picture O(t)=e^{iHt}Oe^{-iHt} spread as time increases. Recent studies have attempted to find features of that spreading which could distinguish between chaotic and integrable dynamics. The operator entanglement-the entanglement entropy in operator space-is a natural candidate to provide such a distinction. Indeed, while it is believed that the operator entanglement grows linearly with time t in chaotic systems, we present evidence that it grows only logarithmically in generic interacting integrable systems. Although this logarithmic growth has been previously established for noninteracting fermions, there has been no progress on interacting integrable systems to date. In this Letter we provide an analytical upper bound on operator entanglement for all local operators in the "Rule 54" qubit chain, a cellular automaton model introduced in the 1990s [Bobenko et al., CMP 158, 127 (1993)CMPHAY0010-361610.1007/BF02097234], and recently advertised as the simplest representative of interacting integrable systems. Physically, the logarithmic bound originates from the fact that the dynamics of the models is mapped onto the one of stable quasiparticles that scatter elastically. The possibility of generalizing this scenario to other interacting integrable systems is briefly discussed.

Nikola Burić, Björn Lyttkens Lindén

Hiroshi Fujisaki, Takayuki Miyadera, Atushi Tanaka

We investigate how the dynamical production of quantum entanglement for weakly coupled, composite quantum systems is influenced by the chaotic dynamics of the corresponding classical system, using coupled kicked tops. The linear entropy for the subsystem (a kicked top) is employed as a measure of entanglement. A perturbative formula for the entanglement production rate is derived. The formula contains a correlation function that can be evaluated only from the information of uncoupled tops. Using this expression and the assumption that the correlation function decays exponentially which is plausible for chaotic tops, it is shown that the increment in the strength of chaos does not enhance the production rate of entanglement when the coupling is weak enough and the subsystems (kicked tops) are strongly chaotic. The result is confirmed by numerical experiments. The perturbative approach is also applied to a weakly chaotic region, where tori and chaotic sea coexist in the corresponding classical phase space, to reexamine a recent numerical study that suggests an intimate relationship between the linear stability of the corresponding classical trajectory and the entanglement production rate.