Increasing entanglement through engineered disorder in the random Ising chain

The ground-state entanglement entropy between block of sites in the random Ising chain is studied by means of the Von Neumann entropy. We show that in presence of strong correlations between the disordered couplings and local magnetic fields the entanglement increases and becomes larger than in the ordered case. The different behavior with respect to the uncorrelated disordered model is due to the drastic change of the ground state properties. The same result holds also for the random three-state quantum Potts model.

Figure 1

(Color online) Block entropy (in bits) averaged over $N=5\times {10}^3$ configurations for an Ising spin chain of $L=200$ sites in the homogeneous (squares) and perfectly correlated random (circles) cases. Best-fit lines with expression (7) are also shown.

Figure 2

(Color online) Prefactor ${\kappa }_2^{\alpha }$ of the entropy versus the correlation coefficient $\alpha$ of the $J$ and $h$ couplings for different chain lengths ($L=50$, black circles; $L=70$, red squares; $L=100$, blue diamonds) and $N={10}^4$ configurations. The solid and dashed line gives ${\kappa }_2^{\alpha =0}=c_2\ln 2\approx 0.35$ and ${\kappa }_2^h=c_2=0.5$, respectively. The inset shows the finite-size scaling of the prefactor with best-fit lines (solid, $\alpha =0$; dotted, $\alpha =0.95$; dashed-dotted, $\alpha =1$). Extrapolation to the thermodynamic limit $1∕L\to 0$ gives ${\kappa }_2^{\alpha =0}=0.30\pm 0.04$ and ${\kappa }_2^{\alpha =1}=0.60\pm 0.01$.

Figure 3

(Color online) Probability distribution for the von Neumann block entropy for a block of length $l=50$ of an $L=100$ chain for $N=5\times {10}^3$ configurations. Left panel: $\alpha =0$ (random uncorrelated case); right panel: $\alpha =1$ (random perfectly correlated case.)

Figure 4

(Color online) Block entropy (in bits) averaged over $N=3\times {10}^3$ configurations for a $d=3$ Potts model of $L=70$ sites in the homogeneous (squares) and perfectly correlated random (circles) cases. Best-fit lines with expression (7) are also shown.