Entanglement of arbitrary spin pairs in finite cyclic XX chains at zero and finite temperature

N. CANOSA; R. ROSSIGNOLI

Camerino, Italia

Conferencia; ITALIAN QUANTUM INFORMATION SCIENCE CONFERENCE; 2008

We evaluate the exact concurrence between any two spins in cyclic XXZ chains  placed in a uniform transverse magnetic field, both at zero and finite temperature,  by means of the Jordan-Wigner transformation plus a 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 aligned state. at low but non-zero     temperatures the entanglement remains non-zero for arbitrarily high fields,  for any pair separation L, although its magnitude decreases exponentially with the  field. It is also demonstrated that all associated limit temperatures approach a  constant non-zero value in this limit. which decreases as 1/L^2 for L << n but exhibit  special finite size effects for distant qubits. Comparison with the behavior of the thermal     pairwise entanglement in fully connected XXZ chains is also discussed.