Thermofield dynamics: Quantum chaos versus decoherence

Quantum chaos imposes universal spectral signatures that govern the thermofield dynamics of a many-body system in isolation. The fidelity between the initial and time-evolving thermofield double states exhibits as a function of time a decay, dip, ramp, and plateau. Sources of decoherence give rise to a nonunitary evolution and result in information loss. Energy dephasing gradually suppresses quantum noise fluctuations and the dip associated with spectral correlations. Decoherence further delays the appearance of the dip and shortens the span of the linear ramp associated with chaotic behavior. The interplay between signatures of quantum chaos and information loss is determined by the competition among the decoherence, dip, and plateau characteristic times, as demonstrated in the stochastic Sachdev-Ye-Kitaev model.

Figure 1

Logarithmic negativity and Rényi entropy of the stochastic SYK model. A log-linear plot of the (a) logarithmic negativity and (b) Rényi entropy ($n=2$) displayed as a function of time for different decoherence coefficients $\gamma$ in the stochastic SYK model with $N=26$ Majorana fermions. The data are built from 100 independent samples and $\beta =1$.

Figure 2

Fidelity of the stochastic SYK model. Top: A log-log plot of fidelity with different decoherence coefficients $\gamma$ in the stochastic SYK model of $N=26$ Majorana fermions. The data were taken by single and 100 independent samples and $\beta =1$. Bottom: The dip time $t_d^{\left(\gamma \right)}$, the plateau time $t_p^{\left(\gamma \right)}$, the decoherence time $\gamma {\tau }_D$, and $\gamma {\tau }_D/t_d$ are shown as functions of $N$. The data were obtained by sampling over 100 independent realizations and $\beta =0.1$.

Figure 3

Spectral form factor of GUE. Analytical Eqs. (B15) and (B28) are in comparison with numerical calculations for $\beta =0,$ 0.1, 1, 2, and $d=10$, 30. The standard deviation of the random variables of $H$ is selected as $\sigma =1/\sqrt{d}$. The numerical calculations use 1000 independent realizations.

Figure 4

Spectral form factor of SYK model. Analytical Eq. (B37) is compared with numerical calculations ($\beta =0.1$).

Figure 5

Fidelity of the stochastic SYK model for different temperatures. A log-log plot of the fidelity of stochastic SYK model ($N=26$) under different temperature. The variation of the temperature has a negligible effect on the dip and plateau time.