Different Measures of Entanglement in Spin Chains

Different measures of entanglement in spin chains are considered. Main example is VBS state, it is important because of measurement based quantum computation. Entanglement spectrum and negativity are considered in the lecture. These measures are calculated analytically in one dimension. In 2D we have only estimates. Lecture follows the papers: http://arxiv.org/abs/1109.4971 and http://arxiv.org/abs/1110.3300 \\[4pt] [1] Heng Fan, Vladimir Korepin, Vwani Roychowdhury, PRL, {\bf vol 93}, (2004), 227203