SebWouters
commented
2 years ago Hi Jonathon,
Your formula is sort-of correct.
CheMPS2 is spin-adapted, which means there is no notion of alpha and beta electrons inside the computations. Say you're targeting a global | Psi > which is spin-1. Then CheMPS2 doesn't particularly single out any of the Ms = +1, 0, or -1 states. It directly works in the irreducible representation of the targeted state during optimization, without consideration of any particular row of the irreducible representation (e.g. any of the Ms = +1, 0 or -1 states).
The RDM which you get is a summed average over all rows of the irreducible representation. For the spin-1 example it would be:
D_pq = ( \sum_{Ms=+1,0,-1} \sum_σ < Psi (S=1, Ms) | a^+_{pσ} a_qσ | Psi (S=1, Ms) > ) / 3The spin-asymmetric data you can extract is noted in https://www.sciencedirect.com/science/article/abs/pii/S0010465515000168, i.e. spin density, spin flip, etc.
Somewhat simplified, you could think about the "state" |Psi> being the Ms = 0 state, having any <a^+{p, up} a{q, up}> = <a^+{p, down} a{q, down}>.
One could, potentially, by multiplying in the CG coefficients, obtain the spin-dependent 1-RDM for a particular state, such as |S=1, Ms=1>. But it's not currently readily exposed, or done with a couple of lines of code. The whole machinery works with reduced operators, baking in any Jordan-Wigner transformations.
Best regards, Sebastian
JonathonMisiewicz
Hello,
I'm one of the Psi4 developers. I'm standardizing density matrices throughout Psi and need to know exactly what the 1RDM delivered by DMRG is. I'm imagining that the 1RDM is given by
D_pq = \sum_σ < Psi | a^pσ_qσ | Psi >, where| Psi >is of course determined by the MPS ansatz of DMRG.I'm willing to change the Psi interface to CheMPS2 to get the alpha and beta blocks, but I'm also content to just leave this as a spin-summed density if CheMPS2 does not support this.