Entanglement between distant qubits in cyclic XX chains

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.

8 pages, 6 figures

References in corpus (3)

• Global entanglement in XXZ chains
• Global thermal entanglement in n-qubit systems
• Separability conditions and limit temperatures for entanglement detection in two qubit Heisenberg XYZ models

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• XY model on the circle: diagonalization, spectrum, and forerunners of the quantum phase transition
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• Description of thermal entanglement with the static path plus random-phase approximation
• Quantum discord and information deficit in spin chains
• Quantum discord and related measures of quantum correlations in XY chains
• Parallel-in-time quantum simulation via Page and Wootters quantum time
• Inducing critical phenomena in spin chains through sparse alternating fields
• Separability and parity transitions in $XYZ$ spin systems under nonuniform fields