MATERA Juan Mauricio
congresos y reuniones científicas
Entanglement and Area Laws in Weakly Correlated states
MATERA, JUAN MAURICIO; ROSSIGNOLI, RAUL; CANOSA, NORMA
Congreso; Workshop & Conference on Geometrical Aspects of Quantum States in Condensed Matter; 2013
In this talk the evaluation of entanglement measures in weakly correlated Gaussian states will be discussed. Approximate expressions for those quantities in terms of the singular values of certain submatrices of the pairwise correlation matrix associated to the state will be presented. These results enable to obtain in a simple way asymptotic expressions and related "area laws" for the entanglement entropy of bipartitions in pure states, as well as for the logarithmic negativity associated with bipartitions and also pairs of arbitrary subsystems. As an illustration, we consider different types of contiguous and noncontiguous blocks in two dimensional lattices. Exact asymptotic expressions are provided for first neighbor and full range couplings, which lead in the first case to area laws depending on the orientation and separation of the blocks. The connection of those results with other kind of systems, including "spin lattices" through the Random Phase Approximation will be also discussed.