Entanglement between distant qubits in cyclic XX chains

N. CANOSA; R. ROSSIGNOLI

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

American Physical Society

Lugar: N.Y.; Año: 2007 vol. 75 p. 323501 - 323508

1050-2947

We evaluate the exact concurrence between any two spins in a cyclic XX chainof n spins placed in a uniform transverse magnetic field, both at zero andfinite temperature, by means of the Jordan-Wigner transformation plus a numberparity projected statistics. It is shown that while at T=0 there is alwaysentanglement between any two spins in a narrow field interval before thetransition to the aligned state, at low but non-zero temperatures theentanglement remains non-zero for arbitrarily high fields, for any pairseparation L, although its magnitude decreases exponentially with the field.It is also demonstrated that all associated limit temperatures approach aconstant non-zero value in this limit, which decreases as $L^{-2}$ for $L\ll n$but exhibit special finite size effects for distant qubits ($L\approx n/2$).Related aspects such as the different behavior of even and oddantiferromagnetic chains, the existence of n ground state transitions and thethermodynamic limit $n\rightarrow\infty$ are also discussed.