Dynamical quantum correlations after sudden quenches

We employ the mean-field approach in the fermionic picture of the spin-$\frac{1}{2}$ $XXZ$ chain to investigate the dynamics of bipartite quantum discord and concurrence under sudden quenching. In this case, when quenching is performed in the anisotropy from an initial value to the critical point, the quantum correlations show periodic cusps in time. Moreover, the first suppression (cusp) in quantum correlations can be explained in terms of the semiclassical picture of quasiparticle propagation. On the other hand, quenching to, as well as away from, the criticality point shows that the long time pairwise quantum discord gets enhanced from its initial state. Finally, we show that, in the gapped region, a quench in the transverse field displays survival of the next-nearest-neighbor quantum discord. Our results provide a further insight into the dynamical behavior of quantum correlations and their connections to quantum criticality.

Figure 1

(a) Quantum discord of nearest-neighbor spin pairs as a function of time $t$ for a quench of anisotropy from ${\mathrm{\Delta }}_I=0.98$ to the critical point ${\mathrm{\Delta }}_F={\mathrm{\Delta }}_c=1$, at zero magnetic field and for different system sizes. For clarifying the position of the first suppression time $T_s$, the arrow indicates $T_s$ for the case of $N=1000$. Note that for the better visibility, the plot of the individual sizes are shifted by a constant value, along the $y$-direction. (b) Scaling of first suppression time versus the system sizes $N$. (c) The ground-state energy ${\varepsilon }_q$ and group velocity of the quasiparticle at the critical point, $v_g$, at zero magnetic field. The quantum discord is measured in bits while the other quantities are dimensionless for this figure and the rest.

Figure 2

Density plots of quantum discord as a function of anisotropy ${\mathrm{\Delta }}_F$ and time for (a) ${\mathrm{\Delta }}_I=0$ and (e) ${\mathrm{\Delta }}_I=1.5$. (c) Quantum discord between the first nearest neighbors as a function of time at zero temperature and zero magnetic field for quench from ${\mathrm{\Delta }}_I=0$ to ${\mathrm{\Delta }}_F=0.5$, 1, 2, 3. The density plots of concurrence as a function of anisotropy ${\mathrm{\Delta }}_F$ and time for (b) ${\mathrm{\Delta }}_I=0$. and (f) ${\mathrm{\Delta }}_I=1.5$. (d) Concurrence between the first nearest neighbors as a function of time at zero temperature and zero magnetic field for quench from ${\mathrm{\Delta }}_I=0$ to ${\mathrm{\Delta }}_F=0.5$, 1, 2, 3. The concurrence is given in terms of ebits and the dimension of other quantities are dimensionless.

Figure 3

Density plots of quantum discord for a quench from ${\mathrm{\Delta }}_I=0$ to ${\mathrm{\Delta }}_F$, versus ${\mathrm{\Delta }}_F$ and time between (a) first nearest neighbors and (b) second nearest neighbors. (c) Density plot of quantum discord between third-nearest-neighbor spins, for a quench from ${\mathrm{\Delta }}_I=1.5$ to ${\mathrm{\Delta }}_F$.

Figure 4

Density plots of quantum discord between first nearest neighbors, $Q_{i,i+1}$, as a function of time $t$ and anisotropy $\mathrm{\Delta }$ at zero temperature, for a quench from (a) $h_I=0.2$, (b) $h_I=0.5$, (c) $h_I=0.8$, (d) $h_I=1.4$, (e) $h_I=1.6$, and (f) $h_I=2$ to $h_F=0$. The density plots of quantum discord for next nearest neighbor, $Q_{i,i+2}$, for a quench from (g) $h_I=0.2$, (h) $h_I=0.5$, (i) $h_I=1.8$, (j) $h_I=1.4$, (k) $h_I=1.6$, and (l) $h_I=2$ to $h_F=0$.

Figure 5

The density plots of concurrence as a function of time, $t$, and anisotropy, $\mathrm{\Delta }$, at zero temperature, for a quench from (a) $h_I=0.2$, (b) $h_I=0.5$, (c) $h_I=0.8$, (d) $h_I=1.4$, (e) $h_I=1.6$, and (f) $h_I=2$ to $h_F=0$.