Entanglement entropy in extended quantum systems
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
A brief review will be given of the use of von Neumann entropy as a measure of entanglement in quantum information theory. It will then be shown how this can be computed in one-dimensional extended systems such as quantum spin chains using ideas of statistical mechanics and quantum field theory. In general the entanglement in the ground state between a linear subsystem of length $\ell$ and the rest of the system is bounded as $\ell\toınfty$, only at a quantum critical point growing like $łog\ell$. However, much more highly entangled states, with entropy $\propto\ell$, can be produced from states of low entanglement by unitary evolution with a quantum critical hamiltonian. Extensions to higher-dimensional systems as well as to other observables such as correlation functions will be mentioned. Some of these effects should be observable in cold atoms in optical lattices.