Factorization and entanglement in general XYZ spin arrays in nonuniform transverse fields

R. ROSSIGNOLI; N. CANOSA; J.M. MATERA

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

AMER PHYSICAL SOC

Año: 2009 vol. 80 p. 623251 - 623256

1050-2947

We determine the conditions for the existence of a pair of degenerate parity breaking separable eigenstates in general arrays of  arbitrary spins connected through  XYZ couplings of arbitrary range and placed in a transverse field, non necessarily uniform.  Sufficient conditions under which they are  ground states are also provided. It is then shown that  in finite chains, the associated definite parity states, which represent the actual ground state in the immediate vicinity of separability, can exhibit entanglement between any two spins regardless of the coupling range  or separation  with the reduced state of any two subsystems equivalent to that of a pair  of qubits in an entangled mixed state. The corresponding concurrences and negativities are exactly determined. The same properties persist in the uniform mixture of both definite parity states. These effects become specially relevant in  systems close to the  XXZ limit. The possibility of field induced alternating separable solutions with controllable entanglement side limits is also discussed. Illustrative numerical results for the negativity between the first and jth spin in an open spin s chain for different values of s and j are as well provided.