# Finding the eigen state of Hamiltonians

**URL:** <https://itensor.discourse.group/t/finding-the-eigen-state-of-hamiltonians/512>\
**Category:** ITensor Julia Questions\
**Tags:** julia, mpo\
**Created:** [November 13, 2022, 4:06pm UTC](https://itensor.discourse.group/t/finding-the-eigen-state-of-hamiltonians/512 "2022-11-13T16:06:13Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![tsegev](https://avatars.discourse-cdn.com/v4/letter/t/5e9695/32.png) [@tsegev](https://itensor.discourse.group/u/tsegev)\
**Post date:** [November 13, 2022, 4:06pm UTC](https://itensor.discourse.group/t/finding-the-eigen-state-of-hamiltonians/512/1 "2022-11-13T16:06:13Z")

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Hey all,  
What I am trying to do is to find the eigen energies of my H. From what I understand psi\_0 from the example below should be the ground state. Is my assumption correct ? If not, how can I extract from my MPO my eigen state in the form of ground state, first excited state, and so on ? and Es are his corresponding eigen energies?

```nohighlight
    H = MPO(H_bath,site)
    H_tensor = prod(H)
    eigen_E, Eigen_S = eigen(H_tensor)
    Es = diag(eigen_E)) 
    ground_state = Eigen_S * ITensor(placeOne(1, dim(inds(Eigen_S)[end])), inds(Eigen_S)[end])
    psi_0=MPS(ground_state,site)
#G = Eigen_S * prime(conj.(Eigen_S), inds(Eigen_S)[end]) 

```

I made a sanity check using G just to see that I am getting the identity, which I got… but, for some reason I not so sure.  
Tomer

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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:** [November 13, 2022, 4:26pm UTC](https://itensor.discourse.group/t/finding-the-eigen-state-of-hamiltonians/512/2 "2022-11-13T16:26:09Z")

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I understand what you’re doing in terms of the code, but could you give a bit more context about why you want to product all your MPO tensors together and use a full diagonalization? DMRG would be a much for efficient way to find the ground state. Is it because you want to also find a large number of excited states too? Or to debug a DMRG calculation?

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**Author:** ![tsegev](https://avatars.discourse-cdn.com/v4/letter/t/5e9695/32.png) [@tsegev](https://itensor.discourse.group/u/tsegev)\
**Post date:** [November 13, 2022, 4:36pm UTC](https://itensor.discourse.group/t/finding-the-eigen-state-of-hamiltonians/512/3 "2022-11-13T16:36:46Z")

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To find the excited state. I used the DMRG calculations for excited states, but I noticed that as I enlarged my Hilbert space it becomes more and more difficult to do so.

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**Author:** ![alexsunny123](https://avatars.discourse-cdn.com/v4/letter/a/51bf81/32.png) [@alexsunny123](https://itensor.discourse.group/u/alexsunny123)\
**Post date:** [November 17, 2022, 10:30am UTC](https://itensor.discourse.group/t/finding-the-eigen-state-of-hamiltonians/512/4 "2022-11-17T10:30:58Z")

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thanks for the awesome information.