User Tools

Site Tools


en:matrix_product_states

Differences

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

Link to this comparison view

Both sides previous revision Previous revision
en:matrix_product_states [2012/03/11 19:56]
Thomas Köhler [Scalar product]
en:matrix_product_states [2012/03/11 20:27] (current)
Thomas Köhler [Application of a MPO]
Line 100: Line 100:
 \begin{align} \begin{align}
 \hat O \lvert \psi \rangle & =  \sum_{\boldsymbol{\sigma},​ \boldsymbol{\sigma^{\prime}},​ \boldsymbol{\sigma^{\prime\prime}}} (W^{\sigma_1\sigma_1^{\prime}}\ldots W^{\sigma_L\sigma_L^{\prime}})(M^{\sigma_1^{\prime\prime}}\cdots M^{\sigma_L^{\prime\prime}})\lvert {\boldsymbol{\sigma}} \rangle \underbrace{\langle {\boldsymbol{\sigma^\prime}} \lvert {\boldsymbol{\sigma^{\prime\prime}}} \rangle}_{\delta_{\sigma^{\prime}\sigma^{\prime\prime}}}\newline \hat O \lvert \psi \rangle & =  \sum_{\boldsymbol{\sigma},​ \boldsymbol{\sigma^{\prime}},​ \boldsymbol{\sigma^{\prime\prime}}} (W^{\sigma_1\sigma_1^{\prime}}\ldots W^{\sigma_L\sigma_L^{\prime}})(M^{\sigma_1^{\prime\prime}}\cdots M^{\sigma_L^{\prime\prime}})\lvert {\boldsymbol{\sigma}} \rangle \underbrace{\langle {\boldsymbol{\sigma^\prime}} \lvert {\boldsymbol{\sigma^{\prime\prime}}} \rangle}_{\delta_{\sigma^{\prime}\sigma^{\prime\prime}}}\newline
-& =  \sum_{\boldsymbol{\sigma},​ \boldsymbol{\sigma^{\prime}}} (W^{\sigma_1\sigma_1^{\prime}}\ldots W^{\sigma_L\sigma_L^{\prime}})(M^{\sigma_1^{\prime\prime}}\cdots M^{\sigma_L^{\prime\prime}})\lvert {\boldsymbol{\sigma}} \rangle \newline+& =  \sum_{\boldsymbol{\sigma},​ \boldsymbol{\sigma^{\prime}}} (W^{\sigma_1\sigma_1^{\prime}}\ldots W^{\sigma_L\sigma_L^{\prime}})(M^{\sigma_1^{\prime}}\cdots M^{\sigma_L^{\prime}})\lvert {\boldsymbol{\sigma}} \rangle \newline
 & =  \sum_{\boldsymbol{\sigma}} \tilde{M}^{\sigma_1}\cdots \tilde{M}^{\sigma_L} \lvert\boldsymbol{\sigma}\rangle = \lvert \tilde\psi\rangle & =  \sum_{\boldsymbol{\sigma}} \tilde{M}^{\sigma_1}\cdots \tilde{M}^{\sigma_L} \lvert\boldsymbol{\sigma}\rangle = \lvert \tilde\psi\rangle
 \end{align} \end{align}
en/matrix_product_states.txt · Last modified: 2012/03/11 20:27 by Thomas Köhler