Dynamics of entanglement in the transverse Ising model

We study the evolution of nearest-neighbor entanglement in the one-dimensional Ising model with an external transverse field. The system is initialized as the so-called thermal ground state of the pure Ising model. We analyze properties of the generation of entanglement for different regions of external transverse fields. We find that the derivative of the time at which the entanglement reaches its first maximum with respect to the reciprocal transverse field has a minimum at the critical point. This is an indicator of quantum phase transition.

Figure 1

The evolution of bipartite entanglement for the initial state being the “thermal ground state” of the Ising model.

Figure 2

(a): The concurrence at different times $t=0.5$, $1.0$, $1.5$, and $2.0$ as a function of $\lambda$ in the region of $t<2.5$. (b): The concurrence at different times $t=4.0$, $5.0$, $6.0$, and $7.0$ as a function of $\lambda$ in the region of $t>3.0$.

Figure 3

(a): The dynamics of entanglement for different reciprocal fields $\lambda =0.2$, $0.4$, $0.6$, and $0.8$, in the region of $\lambda <0.8$. (b): The dynamics of entanglement for different reciprocal fields $\lambda =1.5$ and $3.0$ in the region of $\lambda >1.07$.

Figure 4

The time at which the entanglement reaches its first maximum and its derivative.