# How to obtain the groundstate of a large system(N=20) by the groundstate of a small system (i.e.N=10)with same initial condition

**URL:** <https://itensor.discourse.group/t/how-to-obtain-the-groundstate-of-a-large-system-n-20-by-the-groundstate-of-a-small-system-i-e-n-10-with-same-initial-condition/2019>\
**Category:** DMRG and Numerical Methods\
**Tags:** julia, mps\
**Created:** [September 28, 2024, 1:52am UTC](https://itensor.discourse.group/t/how-to-obtain-the-groundstate-of-a-large-system-n-20-by-the-groundstate-of-a-small-system-i-e-n-10-with-same-initial-condition/2019 "2024-09-28T01:52:02Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![Jren](https://avatars.discourse-cdn.com/v4/letter/j/ecccb3/32.png) [@Jren](https://itensor.discourse.group/u/Jren)\
**Post date:** [September 28, 2024, 1:52am UTC](https://itensor.discourse.group/t/how-to-obtain-the-groundstate-of-a-large-system-n-20-by-the-groundstate-of-a-small-system-i-e-n-10-with-same-initial-condition/2019/1 "2024-09-28T01:52:03Z")

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Hi, all. Like traditional DMRG ， we can obtain the groundstate of a large system( size N) by the groundstate of a small system (size N-2)with same initial condition. How can we realize the same process in ITensor ?

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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:** [September 30, 2024, 12:53pm UTC](https://itensor.discourse.group/t/how-to-obtain-the-groundstate-of-a-large-system-n-20-by-the-groundstate-of-a-small-system-i-e-n-10-with-same-initial-condition/2019/2 "2024-09-30T12:53:02Z")

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We don’t have a function you can call to do that already written in ITensor, but you can use the tools within ITensor such as tensor contraction and SVD decomposition of tensors to write this algorithm.

The most up-to-date version of this kind of algorithm that I know is in the following paper:  
[https://arxiv.org/abs/0804.2509](https://arxiv.org/abs/0804.2509)  
The following review article gives an alternate and simpler view of the same process using the “Vidal canonical gauge” also:  
[https://arxiv.org/abs/1008.3477](https://arxiv.org/abs/1008.3477)

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**Author:** ![Jren](https://avatars.discourse-cdn.com/v4/letter/j/ecccb3/32.png) [@Jren](https://itensor.discourse.group/u/Jren)\
**Post date:** [September 30, 2024, 1:07pm UTC](https://itensor.discourse.group/t/how-to-obtain-the-groundstate-of-a-large-system-n-20-by-the-groundstate-of-a-small-system-i-e-n-10-with-same-initial-condition/2019/3 "2024-09-30T13:07:16Z")

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> [@miles](#):
>
> contraction

OK, thanks!