mirror of
https://github.com/TREX-CoE/trexio.git
synced 2024-08-25 06:31:43 +02:00
Removed RDM down-up which was redundant with up-down
This commit is contained in:
parent
fb711e1bed
commit
87035ba5c8
21
trex.org
21
trex.org
@ -1043,8 +1043,7 @@ power = [
|
||||
\gamma_{ij} = \gamma^{\uparrow}_{ij} + \gamma^{\downarrow}_{ij}
|
||||
\]
|
||||
|
||||
The $\uparrow \uparrow$, $\downarrow \downarrow$, $\uparrow \downarrow$, $\downarrow \uparrow$
|
||||
components of the two-body density matrix are given by
|
||||
The $\uparrow \uparrow$, $\downarrow \downarrow$, $\uparrow \downarrow$ components of the two-body density matrix are given by
|
||||
\begin{eqnarray*}
|
||||
\Gamma_{ijkl}^{\uparrow \uparrow} &=&
|
||||
\langle \Psi | \hat{a}^{\dagger}_{k\alpha}\, \hat{a}^{\dagger}_{l\alpha} \hat{a}_{j\alpha}\, \hat{a}_{i\alpha} | \Psi \rangle \\
|
||||
@ -1052,15 +1051,19 @@ power = [
|
||||
\langle \Psi | \hat{a}^{\dagger}_{k\beta}\, \hat{a}^{\dagger}_{l\beta} \hat{a}_{j\beta}\, \hat{a}_{i\beta} | \Psi \rangle \\
|
||||
\Gamma_{ijkl}^{\uparrow \downarrow} &=&
|
||||
\langle \Psi | \hat{a}^{\dagger}_{k\alpha}\, \hat{a}^{\dagger}_{l\beta} \hat{a}_{j\beta}\, \hat{a}_{i\alpha} | \Psi \rangle \\
|
||||
\Gamma_{ijkl}^{\downarrow \uparrow} &=&
|
||||
\langle \Psi | \hat{a}^{\dagger}_{k\beta}\, \hat{a}^{\dagger}_{l\alpha} \hat{a}_{j\alpha}\, \hat{a}_{i\beta} | \Psi \rangle \\
|
||||
\end{eqnarray*}
|
||||
and the spin-summed one-body density matrix is
|
||||
\[
|
||||
\Gamma_{ijkl} = \Gamma_{ijkl}^{\uparrow \uparrow} +
|
||||
\Gamma_{ijkl}^{\downarrow \downarrow} + \Gamma_{ijkl}^{\uparrow \downarrow} +
|
||||
\Gamma_{ijkl}^{\downarrow \uparrow}
|
||||
\Gamma_{ijkl}^{\downarrow \downarrow} + \Gamma_{ijkl}^{\uparrow \downarrow}.
|
||||
\]
|
||||
The density matrices are normalized such that
|
||||
\begin{eqnarray*}
|
||||
\sum_{ij} \Gamma_{ijij}^{\uparrow \uparrow} & = & N_\uparrow\, (N_\uparrow-1)/2 \\
|
||||
\sum_{ij} \Gamma_{ijij}^{\downarrow \downarrow} & = & N_\downarrow\, (N_\downarrow-1)/2 \\
|
||||
\sum_{ij} \Gamma_{ijij}^{\uparrow \downarrow} & = & N_\uparrow\, N_\downarrow \\
|
||||
\sum_{ij} \Gamma_{ijij} & = & (N_\uparrow+N_\downarrow)\, (N_\uparrow+N_\downarrow-1)/2.
|
||||
\end{eqnarray*}
|
||||
|
||||
The total energy can be computed as:
|
||||
\[
|
||||
@ -1094,7 +1097,6 @@ power = [
|
||||
| ~2e_upup~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \uparrow\uparrow component of the two-body reduced density matrix |
|
||||
| ~2e_dndn~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \downarrow\downarrow component of the two-body reduced density matrix |
|
||||
| ~2e_updn~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \uparrow\downarrow component of the two-body reduced density matrix |
|
||||
| ~2e_dnup~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \downarrow\uparrow component of the two-body reduced density matrix |
|
||||
| ~2e_cholesky_num~ | ~dim~ | | Number of Cholesky vectors |
|
||||
| ~2e_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_cholesky_num)~ | Cholesky decomposition of the two-body RDM (spin trace) |
|
||||
| ~2e_upup_cholesky_num~ | ~dim~ | | Number of Cholesky vectors |
|
||||
@ -1103,8 +1105,6 @@ power = [
|
||||
| ~2e_dndn_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_dndn_cholesky_num)~ | Cholesky decomposition of the two-body RDM (\downarrow\downarrow) |
|
||||
| ~2e_updn_cholesky_num~ | ~dim~ | | Number of Cholesky vectors |
|
||||
| ~2e_updn_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_updn_cholesky_num)~ | Cholesky decomposition of the two-body RDM (\uparrow\downarrow) |
|
||||
| ~2e_dnup_cholesky_num~ | ~dim~ | | Number of Cholesky vectors |
|
||||
| ~2e_dnup_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_dnup_cholesky_num)~ | Cholesky decomposition of the two-body RDM (\downarrow\uparrow) |
|
||||
|
||||
#+CALL: json(data=rdm, title="rdm")
|
||||
|
||||
@ -1119,7 +1119,6 @@ power = [
|
||||
, "2e_upup" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
|
||||
, "2e_dndn" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
|
||||
, "2e_updn" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
|
||||
, "2e_dnup" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
|
||||
, "2e_cholesky_num" : [ "dim" , [] ]
|
||||
, "2e_cholesky" : [ "float sparse", [ "rdm.2e_cholesky_num", "mo.num", "mo.num" ] ]
|
||||
, "2e_upup_cholesky_num" : [ "dim" , [] ]
|
||||
@ -1128,8 +1127,6 @@ power = [
|
||||
, "2e_dndn_cholesky" : [ "float sparse", [ "rdm.2e_dndn_cholesky_num", "mo.num", "mo.num" ] ]
|
||||
, "2e_updn_cholesky_num" : [ "dim" , [] ]
|
||||
, "2e_updn_cholesky" : [ "float sparse", [ "rdm.2e_updn_cholesky_num", "mo.num", "mo.num" ] ]
|
||||
, "2e_dnup_cholesky_num" : [ "dim" , [] ]
|
||||
, "2e_dnup_cholesky" : [ "float sparse", [ "rdm.2e_dnup_cholesky_num", "mo.num", "mo.num" ] ]
|
||||
} ,
|
||||
#+end_src
|
||||
:end:
|
||||
|
Loading…
Reference in New Issue
Block a user