Entanglement of finite cyclic chains at factorizing fields

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

Buenos Aires

Workshop; Low dimensional condensed matter Eleventh J. J. Giambiagi Winter School.; 2010

CONICET-UBA

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 magnetic field, not 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 pair of qubits in an entangled mixed state. The exact side limits of the entanglement between any two subsystems, including those for the block entropy and those for any two spins or group of spins at the separability point, are determined analytically for any value of the spin. The same properties are shown to persist in the 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. As application, we examine the previous features in dimerized spin chains, showing that in the vicinity of separability the system looses all signatures of dimerization, with pairwise entanglement approaching infinite range and becoming independent of separation and coupling range. Illustrative numerical results for the negativity between two spins in an open spin s chain for different values of s and the separation are as well provided.