## Learn to Use ITensor

# 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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