[ITensors] Support for permutation symmetric tensors

[Krzmbrzl]

I have read the ITensors paper and also searched through the online documentation, but I am still not sure whether the ITensors has support for permutational symmetry of indices. For instance, consider the very simple case of $f_{ai} = f_{ia}$: can I tell the package about this symmetry such that it can deduce that it only needs to actually store (and process) a subset of the full $f_{ai}$ matrix?

I've read that the library supports quantum numbers that lead to block-sparse representations and can encode things like rotational symmetry of the underlying problem, but (at least to my understanding) these kinds of symmetries are orthogonal to permutational symmetry of a tensor's indices.

As an example in which this becomes relevant is Coupled Cluster theory (in the context of quantum chemistry) where one has to compute a "residual" that is e.g. $R^{ab}{ij}$ and which has the symmetry $R^{ab}{ij} = R^{ba}_{ji}$ (in the so-called "spin-summed" form).

[mtfishman]

We don't support that right now and don't have immediate plans to support it, but maybe at some point we will.

Something you will be able to do relatively soon (when we complete our rewrite of NDTensors as outlined in #1250) is if you or an external Julia package defines an AbstractArray subtype that has permutation symmetry, you will be able to wrap it in an ITensor and use it in ITensor functionality. It would have to define some minimal interface to be used in ITensor operations.

[Krzmbrzl]

Alright, thank you very much for the clarification 👍

[mtfishman]

We can keep this open for others to find.