# MPS Applet

### Site Tools

en:matrix_product_states

# Differences

This shows you the differences between two versions of the page.

 en:matrix_product_states [2012/03/11 20:27]127.0.0.1 external edit en:matrix_product_states [2019/06/04 21:37] (current)thomas 2019/06/04 21:37 thomas 2012/03/11 20:27 external edit 2019/06/04 21:37 thomas 2012/03/11 20:27 external edit Line 25: Line 25: To get an MPS from a known quantum state with coefficients $c_{\sigma_1\ldots\sigma_L}$ we have to shuffle the $2^L$ coefficients into a matrix $c^\prime$ of dimension $2 \times 2^{L-1}$. To get an MPS from a known quantum state with coefficients $c_{\sigma_1\ldots\sigma_L}$ we have to shuffle the $2^L$ coefficients into a matrix $c^\prime$ of dimension $2 \times 2^{L-1}$. - {{ :​createmps-01.png?​400|}} + {{ :wiki:​createmps-01.png?​400|}} \begin{align} \begin{align} Line 49: Line 49: One continues with an svd on $c_{(a_1\sigma_2),​(\sigma_3\ldots\sigma_L)}^{\prime\prime}$. The new $S$ and $V^\dagger$ will again be combined and reshuffled into two $A$-matrices. The new coefficients are now: One continues with an svd on $c_{(a_1\sigma_2),​(\sigma_3\ldots\sigma_L)}^{\prime\prime}$. The new $S$ and $V^\dagger$ will again be combined and reshuffled into two $A$-matrices. The new coefficients are now: - $A^{\sigma_2}_{a_1,​a_2} = U_{(a_1\sigma_2),​ a_2}$. This procedure is repeated ​untill ​site $L-1$ is reached. One finally obtains: + $A^{\sigma_2}_{a_1,​a_2} = U_{(a_1\sigma_2),​ a_2}$. This procedure is repeated ​until site $L-1$ is reached. One finally obtains: