## Learn to Use ITensor

main / formulas / itensor_replace_index

# Replace an Index of an ITensor with Another Index

Say we have an ITensor with indices a,b,c (objects of type Index):

auto T = ITensor(a,b,c);


and we want to replace the Index b with another Index x.

To do this we can use a delta tensor, which models an identity matrix or a Kronecker delta symbol. To create a delta tensor, use the function delta:

T = T * delta(b,x);


Now T will have the index x instead of b, but otherwise the same data. The Index x should be chosen to have the same dimension as b.

Internally, creating a two-index delta tensor does not allocate any storage in memory and contracting it with another tensor uses an efficient algorithm that just substitutes one index for another.

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