Entanglement between distant qubits in cyclic XX chains,

N. CANOSA; R. ROSSIGNOLI

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

APS

Lugar: New York; 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, at both zero and finite temperature by means of  the Jordan-Wigner transformation plus a number  parity projected statistics. It is shown that while at T=0 there is always entanglement between any two spins in a narrow field interval before the transition to the alignedstate, at  low but non-zero temperatures, the entanglement remains non-zero forarbitrary high fields for any pair separation L, although its magnitude decreases exponentially with increasing  field. It is also demonstrated that  the associated limittemperatures approach a constant non-zero value in this limit, which  decreases asL-2 , for L < n, but exhibits special finite size effects for distant qubits (L @ n/2). Related aspects such as the different behavior of even and odd antiferromagnetic chains,the existence of n ground state transitions, and the thermodynamic limit are alsodiscussed.