# set up Hubbard Holstein model

**URL:** <https://itensor.discourse.group/t/set-up-hubbard-holstein-model/963>\
**Category:** ITensor Julia Questions\
**Tags:** julia, dmrg\
**Created:** [June 22, 2023, 11:14pm UTC](https://itensor.discourse.group/t/set-up-hubbard-holstein-model/963 "2023-06-22T23:14:20Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![abinitio](https://avatars.discourse-cdn.com/v4/letter/a/c77e96/32.png) [@abinitio](https://itensor.discourse.group/u/abinitio)\
**Post date:** [June 22, 2023, 11:14pm UTC](https://itensor.discourse.group/t/set-up-hubbard-holstein-model/963/1 "2023-06-22T23:14:20Z")

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Hello,

I am new to iTensor and trying to implement the Hubbard-Holstein model,

H=-t\sum\_{i,\sigma}[c^{\dagger}\_{i,\sigma}c\_{i+1,\sigma}+H.C]+U\sum\_{i}n\_{i,\uparrow}n\_{i,\downarrow}+\omega\_{0}\sum\_{i}b\_{i}^{\dagger}b\_{i}+g\sum\_{i}n\_{i}(b\_{i}+b\_{i}^{\dagger}).

I am using the Julia version of iTensor.  
Can anyone help me setting up the mixed site type that we need to implement the Hubbard Holstein model?

Thank you

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**Author:** ![miles](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/miles/32/6_2.png) [@miles](https://itensor.discourse.group/u/miles)\
**Post date:** [June 23, 2023, 2:16pm UTC](https://itensor.discourse.group/t/set-up-hubbard-holstein-model/963/2 "2023-06-23T14:16:23Z")

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Hi @abinitio,  
Here is a previous discussion where I gave a code example of how to create a “sites” array that contains a mixture of Electron and Boson sites:  
[https://itensor.discourse.group/t/mixed-site-set-with-quantum-number-conservation/470/2](https://itensor.discourse.group/t/mixed-site-set-with-quantum-number-conservation/470/2)

Does that address your question?

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<div class="post-metadata">

**Author:** ![abinitio](https://avatars.discourse-cdn.com/v4/letter/a/c77e96/32.png) [@abinitio](https://itensor.discourse.group/u/abinitio)\
**Post date:** [June 23, 2023, 6:40pm UTC](https://itensor.discourse.group/t/set-up-hubbard-holstein-model/963/3 "2023-06-23T18:40:14Z")

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Thanks, Miles. This will be very helpful.