# define initial translation-invariant state
**URL:** https://itensor.discourse.group/t/define-initial-translation-invariant-state/1980
**Category:** ITensor Julia Questions
**Tags:** julia
**Created:** [September 12, 2024, 1:27pm UTC](https://itensor.discourse.group/t/define-initial-translation-invariant-state/1980 "2024-09-12T13:27:59Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@AbraDabra](https://itensor.discourse.group/u/AbraDabra)
#### Post date: [September 12, 2024, 1:27pm UTC](https://itensor.discourse.group/t/define-initial-translation-invariant-state/1980/1 "2024-09-12T13:27:59Z")
Hi, How one can create initial product state of the form:
\psi = \psi\_0 \otimes \psi\_0 \ldots \psi\_0,
where \psi\_0 = \cos(\theta) |Up\rangle + \sin(\theta) |Dn\rangle
similar question was posted in [Setting Random Initial Product State - ITensor Support Q&A](https://itensor.org/support/1357/setting-random-initial-product-state)
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### Author:  [@miles](https://itensor.discourse.group/u/miles)
#### Post date: [September 12, 2024, 2:31pm UTC](https://itensor.discourse.group/t/define-initial-translation-invariant-state/1980/2 "2024-09-12T14:31:23Z")
The code below ought to work
```julia
N = 10
sites = siteinds(“S=1/2”,N)
psi = MPS(sites)
for j=1:N
psi[j] = ITensor([cos(theta), sin(theta)], sites[j])
end
orthogonalize!(psi,1) # not strictly necessary but will put in link indices and may help later functions to work correctly
```
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### Author:  [@AbraDabra](https://itensor.discourse.group/u/AbraDabra)
#### Post date: [September 12, 2024, 2:53pm UTC](https://itensor.discourse.group/t/define-initial-translation-invariant-state/1980/3 "2024-09-12T14:53:41Z")
Many thanks!
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### Author:  [@system](https://itensor.discourse.group/u/system)
#### Post date: [September 22, 2024, 2:53pm UTC](https://itensor.discourse.group/t/define-initial-translation-invariant-state/1980/4 "2024-09-22T14:53:49Z")
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