Calculating reduced density matrix of each site

[Shovan-Physics]

Is there an efficient way to get the reduced density matrix of each site? For example, if I want the distribution over the local basis states (in the Bose-Hubbard model), currently I am defining projectors onto each of the basis states, forming MPO with each projector, and calculating their expectation values, which is rather clumsy and repetitive.

[hczhai]

This is solved in #122 using custom operators.

[Shovan-Physics]

Thanks for the update. Although it makes the calculation faster, it doesn't quite solve this problem:

Suppose I have 6 local basis states (as in the Bose-Hubbard model with NB_MAX = 5) and I want to get the 6 x 6 reduced density matrix of each site (e.g., to compare with a Gutzwiller ansatz). Currently, I need to define 20 on-site operators and run get_npdm for each of them to get all the independent matrix elements.

However, if we could align the MPS center at a site and contract all other site and bond indices we could get the density matrix $\rho^{(j)}_{\sigma, \sigma^{\prime}}$ at one go. Is this possible to do? I know there is a command align_mps_center but I don't know how to get/contract the indices.

[hczhai]

You can simply do

dms = driver.get_npdm(mps, npdm_expr=['N', 'M', 'L', 'K', 'J', 'I'], fermionic_ops='')

which will generate results of

dms = [
    *driver.get_npdm(mps, npdm_expr='N', fermionic_ops=''),
    *driver.get_npdm(mps, npdm_expr='M', fermionic_ops=''),
    ...
    *driver.get_npdm(mps, npdm_expr='I', fermionic_ops=''),
]

at one time.

[Shovan-Physics]

That helps, thanks. Do we need to use a single letter for each operator? I tried using 'P0','P1','P2'.. as well as '0','1','2'.. but got error. Wondering in case I run out of the alphabet.

[hczhai]

Numbers have special meaning in SU(2) strings so they cannot be used for operators.

Wondering in case I run out of the alphabet.

You can define a subset of your operators, call driver.get_npdm, then redefine site_ops for the remaining operators, and call driver.get_npdm, etc.

[Shovan-Physics]

OK thanks.