%0 Book Section %1 statphys23_1098 %A Lin, Y.C. %A Igloi, F. %A Rieger, H. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K critical dimensions disordered entanglement entropy higher points quantum statphys23 topic-8 %T Entanglement Entropy at Infinite-Randomness Fixed Points in Higher Dimensions %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=1098 %X Ground state entanglement quantified using the von Neumann entropy is known to obey a universal scaling law in some one-dimensional critical spin systems with and without disorder. The scaling behavior of the entanglement entropy in higher dimensions is far less clear. This poster contribution will present our findings in the entanglement entropy of the random quantum Ising model in two dimensions, obtained by a numerical implementation of the strong disorder renormalization group. Our results show that the asymptotic behavior of the entropy per surface area diverges at and only at the quantum phase transition that is governed by an infinite-randomness fixed point. Here we identify a double-logarithmic multiplicative correction to the area law for the entanglement entropy. For the diluted quantum Ising model in higher dimensions, the pure area law is found to be valid at the percolation threshold, also governed by infinite randomness. The structure of the strongly correlated spin clusters observed in the ground state of the random quantum Ising model is fundamentally different from the one in the diluted case, which reflects the different degrees of quantum entanglement of the two systems.

@incollection{statphys23_1098, abstract = {Ground state entanglement quantified using the von Neumann entropy is known to obey a universal scaling law in some one-dimensional critical spin systems with and without disorder. The scaling behavior of the entanglement entropy in higher dimensions is far less clear. This poster contribution will present our findings in the entanglement entropy of the random quantum Ising model in two dimensions, obtained by a numerical implementation of the strong disorder renormalization group. Our results show that the asymptotic behavior of the entropy per surface area diverges at and only at the quantum phase transition that is governed by an infinite-randomness fixed point. Here we identify a {\it double-logarithmic} multiplicative correction to the area law for the entanglement entropy. For the diluted quantum Ising model in higher dimensions, the pure area law is found to be valid at the percolation threshold, also governed by infinite randomness. The structure of the strongly correlated spin clusters observed in the ground state of the random quantum Ising model is fundamentally different from the one in the diluted case, which reflects the different degrees of quantum entanglement of the two systems.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Lin, Y.C. and Igloi, F. and Rieger, H.}, biburl = {https://www.bibsonomy.org/bibtex/29b2469418b6cbeb1465571ef455bdf64/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {1b2f558d57bd0da999cb8d7a0381de1d}, intrahash = {9b2469418b6cbeb1465571ef455bdf64}, keywords = {critical dimensions disordered entanglement entropy higher points quantum statphys23 topic-8}, month = {9-13 July}, timestamp = {2007-06-20T10:16:39.000+0200}, title = {Entanglement Entropy at Infinite-Randomness Fixed Points in Higher Dimensions}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=1098}, year = 2007 }