Entanglement between distant qubits in XXZ spin chains

N. CANOSA; R. ROSSIGNOLI

Paraty, Brasil,

Workshop; II QUANTUM INFORMATION SCHOOL AND WORKSHOP.; 2009

CNPq - Institute for Quantum Computing

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.