Quantum and classical thermal correlations in the $\mathit{XY}$ spin-$\frac{1}{2}$ chain

We investigate pairwise quantum correlation as measured by the quantum discord as well as its classical counterpart in the thermodynamic limit of anisotropic $\mathit{XY}$ spin-$1/2$ chains in a transverse magnetic field for both zero and finite temperatures. Analytical expressions for both classical and quantum correlations are obtained for spin pairs at any distance. In the case of zero temperature, it is shown that the quantum discord for spin pairs farther than second neighbors is able to characterize a quantum phase transition, even though pairwise entanglement is absent for such distances. For finite temperatures, we show that quantum correlations can be increased with temperature in the presence of a magnetic field. Moreover, in the $\mathit{XX}$ limit, thermal quantum discord is found to be dominant over classical correlation while the opposite scenario takes place for the transverse field Ising model limit.

Figure 1

Quantum phase diagram for the anisotropic $\mathit{XY}$ spin-1/2 chain. The $\mathit{XX}$ model obtained by setting $\gamma =0$ displays a critical line for $\lambda \in [0,1]$. The Ising model obtained for $\gamma =1$ exhibits a critical point at $\lambda =1$.

Figure 2

Quantum discord between (a) first, (b) second, (c) third, and (d) fourth nearest neighbors and entanglement of formation between (e) third and (f) fourth nearest neighbors as a function of anisotropy ($\gamma$) and $\lambda$ at zero temperature.

Figure 3

Derivative of the quantum discord between fourth nearest neighbors with respect to $\lambda$ at zero temperature.

Figure 4

Derivative of the classical correlation between fourth nearest neighbors with respect to $\lambda$ at zero temperature.

Figure 5

(a) Classical and (b) quantum correlations between second nearest neighbors in the $\mathit{XX}$ model as a function of temperature ($\mathit{kT}$) and inverse of the magnetic field ($\lambda$).

Figure 6

(a) Classical and (b) quantum correlations between second nearest neighbors in the transverse Ising model as a function of temperature ($\mathit{kT}$) and inverse of the magnetic field ($\lambda$).