# Best Method to Generate Haar Random States for a Spin-1/2 Chain?

**URL:** <https://itensor.discourse.group/t/best-method-to-generate-haar-random-states-for-a-spin-1-2-chain/2135>\
**Category:** ITensor Julia Questions\
**Tags:** entanglement, mps\
**Created:** [November 25, 2024, 10:16am UTC](https://itensor.discourse.group/t/best-method-to-generate-haar-random-states-for-a-spin-1-2-chain/2135 "2024-11-25T10:16:59Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![ktrdcp](https://avatars.discourse-cdn.com/v4/letter/k/dbc845/32.png) [@ktrdcp](https://itensor.discourse.group/u/ktrdcp)\
**Post date:** [November 25, 2024, 10:16am UTC](https://itensor.discourse.group/t/best-method-to-generate-haar-random-states-for-a-spin-1-2-chain/2135/1 "2024-11-25T10:16:59Z")

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I am trying to generate a Haar random state for a spin-1/2 chain of length 3. My goal is to sample a truly Haar random pure state in the Hilbert space of the chain.

I have considered using `randomMPS` with a sufficiently large bond dimension. However, I am uncertain if this approach correctly samples from the Haar measure over the full Hilbert space.

Is `randomMPS` appropriate for this purpose? Or is there a better method available within ITensor to generate such Haar random states for a finite chain?

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**Author:** ![mtfishman](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/mtfishman/32/11_2.png) [@mtfishman](https://itensor.discourse.group/u/mtfishman)\
**Post date:** [November 25, 2024, 1:19pm UTC](https://itensor.discourse.group/t/best-method-to-generate-haar-random-states-for-a-spin-1-2-chain/2135/2 "2024-11-25T13:19:50Z")

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> [@ktrdcp](#):
>
> I am trying to generate a Haar random state for a spin-1/2 chain of length 3.

If the state is length 3, why do you need an MPS? Can’t you just represent the entire state as a tensor and generate random tensors?