Keeping indices in place after apply

[jwnys]

Hi, I'm (very) new to itensor(MPS), so apologies if this is a straightforward question/answer, but can't find the answer in the docs.
I've got an MPS with two site indices per tensor (call them P and A indices).

MPS
[1] ((dim=2|id=276|"P,S=1/2,Site,n=1"), (dim=2|id=189|"A,S=1/2,Site,n=1"), (dim=1|id=565|"Link,l=1"))
[2] ((dim=2|id=654|"P,S=1/2,Site,n=2"), (dim=2|id=260|"A,S=1/2,Site,n=2"), (dim=1|id=107|"Link,l=2"), (dim=1|id=565|"Link,l=1"))
[3] ((dim=2|id=74|"P,S=1/2,Site,n=3"), (dim=2|id=873|"A,S=1/2,Site,n=3"), (dim=1|id=462|"Link,l=3"), (dim=1|id=107|"Link,l=2"))
[4] ((dim=2|id=937|"P,S=1/2,Site,n=4"), (dim=2|id=670|"A,S=1/2,Site,n=4"), (dim=1|id=462|"Link,l=3"))

I want to apply an MPO on the P indices only (it's defined with P indices only).
After apply or contract, I get an MPS where all A indices are on site 1.

MPS
[1] ((dim=2|id=670|"A,S=1/2,Site,n=4"), (dim=2|id=873|"A,S=1/2,Site,n=3"), (dim=2|id=260|"A,S=1/2,Site,n=2"), (dim=3|id=680|"Link,l=1")', (dim=2|id=189|"A,S=1/2,Site,n=1"), (dim=2|id=276|"P,S=1/2,Site,n=1")')
[2] ((dim=2|id=654|"P,S=1/2,Site,n=2")', (dim=3|id=267|"Link,l=2")', (dim=3|id=680|"Link,l=1")')
[3] ((dim=2|id=74|"P,S=1/2,Site,n=3")', (dim=2|id=664|"Link,l=3")', (dim=3|id=267|"Link,l=2")')
[4] ((dim=2|id=937|"P,S=1/2,Site,n=4")', (dim=2|id=664|"Link,l=3")')

Is there a way to keep the A indices attached to the original sites, to avoid errors related to site index mismatches later?

Thanks, Jannes

[mtfishman]

It sounds like you should convert the MPS to an MPO and then perform that operation as an MPO-MPO contraction. The MPO-MPS contraction/application code assumes that all of the indices of the MPS are contracted with the MPO, the behavior you are seeing is basically an accident (I'm surprised it works as well as it did...).

[jwnys]

Ok, I see, from the docs, I understood that a site can have any number of indices in general.
The goal here was to represent operators as doubled states, since this simplifies my formalism a lot.
My current hack is to simply apply an identity MPO to the P indices of the bra to bring them in the same form, but it is quite fishy.
Are you saying that this should fail and this approach is to be avoided entirely?
My assumption was that the ITensor index contraction should not care about whether I contract all indices or a subset?
Thanks in advance.

[mtfishman]

Generally it is fine to have MPS with more than one site index, but the MPO-MPS code is written in a way where it assumes that all of the MPS site indices are contracted with the MPO. For contractions with dangling site indices, you can just reinterpret the MPS as an MPO (i.e. make an MPO that has the same tensors as the MPS you defined) and then do MPO-MPO contraction.