Entanglement generation resonances in XY chains

RAÚL DANTE ROSSIGNOLI; CHRISTIAN TOMÁS SCHMIEGELOW

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

AMER PHYSICAL SOC

Año: 2007 vol. 75 p. 12320 - 12329

1050-2947

   We examine the maximum entanglement reached by an initially fully aligned state evolving in an XY Heisenberg spin chain placed in a uniform transverse magnetic field. Both the global entanglement between one qubit and the rest of the chain and the pairwise entanglement between adjacent qubits is analyzed. It is shown that in both cases the maximum is not a monotonous decreasing function of the aligning field, exhibiting instead a resonant behavior for low anisotropies, with pronounced peaks (a total of n / 2 peaks in the globalentanglement for an n-spin chain) , whose width is proportional to the anisotropy and whose height remains finite in the limit of small anisotropy. It is also seen that the maximum pairwise entanglement is not a smooth function of the field even in small finite chains, where it may exhibit narrow peaks above strict plateaus. Explicit analytical results for small chains, as well as general exact results for finite n-spin chains obtained through the Jordan-Wigner mapping, are discussed.