en:matrix_product_states

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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 |
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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} | ||

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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: |

en/matrix_product_states.txt ยท Last modified: 2019/06/04 21:37 by thomas