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arXiv · 0906.0801

Entanglement between distant qubits in cyclic XX chains

N. Canosa·R. Rossignoli
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Abstract

We evaluate the exact concurrence between any two spins in a cyclic XX chain of n spins placed in a uniform transverse magnetic field, both at 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 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 (L approx. 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 also discussed.

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N. Canosa, R. Rossignoli. 2009-06-04. Entanglement between distant qubits in cyclic XX chains. https://doi.org/10.1103/physreva.75.032350

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