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

ITensor Julia Questions
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1

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?

2

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?