Evaluation of entanglement observables in spin systems and its estimation by means of RPA

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

Paraty

Workshop; III Quantum Information School and workshop - Paraty 2011; 2011

CNPq

We examine the entanglement entropy of the even half of a translationally invariant finite chain or lattice in its ground state. This entropy (“comb entropy”) measures the entanglement between the even and odd halves and can be expected to be extensive for short-range couplings away from criticality.We first consider bosonic systems with quadratic couplings, where analytic expressions for arbitrary dimensions can be provided. By means of the random-phase approximation the previous treatment is then applied to finite spin chains and arrays. Results obtained for first-neighbor anisotropic XY couplings indicate that at strong magnetic fields this entropy is strictly extensive, although at weak fields important deviations arise due to parity-breaking effects and the presence of a factorizing field (in the vicinity of which it becomes size-independent and identical). For small spin s chains the bosonic random-phase approximation predictions are in agreement with the exact numerical results.