CONICET | Buscador de Institutos y Recursos Humanos

The study of quantum entanglement in many-body systems is of great importance for both quantum information science and condensed matter physics. In this contribution we describe some recent developments [1] for evaluating entanglement observables in general interacting quantum many-body systems and in particular in quantum spin systems. Based on the path integral representation of the partition function obtained through the Hubbard-Stratonovich transformation and a proper treatment of the different contributions to the path integral, a robust yet tractable general approximation scheme is derived, which contains as a particular case the so-called random phase approximation. This allows to relate the entanglement properties of general systems to those in more simple and solvable systems, where they can be more easily evaluated, like bosonic systems with quadratic interactions. Results for different entanglement observables such as the pairwise concurrence, the block entropy and the negativity between arbitrary subsystems are shown for different spin systems and compared with exact results when available. [1] J.M. Matera, R. Rossignoli, N. Canosa, Phys. Rev. A 82, 052332 (2010); Phys. Rev. A 78, 042319 (2008).