# Multi-point correlation function using ITensor DMRG

**URL:** <https://itensor.discourse.group/t/multi-point-correlation-function-using-itensor-dmrg/2238>\
**Category:** DMRG and Numerical Methods\
**Tags:** julia, dmrg\
**Created:** [February 10, 2025, 6:23am UTC](https://itensor.discourse.group/t/multi-point-correlation-function-using-itensor-dmrg/2238 "2025-02-10T06:23:45Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![ZAHID-8017](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/zahid-8017/32/702_2.png) [@ZAHID-8017](https://itensor.discourse.group/u/ZAHID-8017)\
**Post date:** [February 10, 2025, 6:23am UTC](https://itensor.discourse.group/t/multi-point-correlation-function-using-itensor-dmrg/2238/1 "2025-02-10T06:23:45Z")

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Dear All,

ITensor provides a function that computes correlation function matrix for two operators A\_{i}, B\_{i}.  
That is C[i, j] = correlation\_matrix(psi, A\_{i}, B\_{i}).

How can I compute a multi-point correlation quantity, for instance, C[i, j, k, l]?

Could you please help me with this? also how to implement it using DMRGObserver?

And I apologize for asking the naive question.

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**Author:** ![ryanlevy](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/ryanlevy/32/150_2.png) [@ryanlevy](https://itensor.discourse.group/u/ryanlevy)\
**Post date:** [February 10, 2025, 12:20pm UTC](https://itensor.discourse.group/t/multi-point-correlation-function-using-itensor-dmrg/2238/2 "2025-02-10T12:20:45Z")

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There is unfortunately limited support for general C\_ijkl, but some things are implemented in this package:

> **[GitHub - ITensor/ITensorCorrelators.jl](https://github.com/ITensor/ITensorCorrelators.jl)**
>
> Contribute to ITensor/ITensorCorrelators.jl development by creating an account on GitHub.

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**Author:** ![ZAHID-8017](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/zahid-8017/32/702_2.png) [@ZAHID-8017](https://itensor.discourse.group/u/ZAHID-8017)\
**Post date:** [February 10, 2025, 1:17pm UTC](https://itensor.discourse.group/t/multi-point-correlation-function-using-itensor-dmrg/2238/3 "2025-02-10T13:17:24Z")

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Thanks you so much for the quick response

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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:** [February 18, 2025, 12:42am UTC](https://itensor.discourse.group/t/multi-point-correlation-function-using-itensor-dmrg/2238/4 "2025-02-18T00:42:46Z")

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Also, Zahid, if you are interested in a way to implement multi-point correlators yourself (say of the form \langle\psi| A\_i B\_j C\_k |\psi\rangle), one thing you can try is to first multiply A\_i into your state |\psi'\_i\rangle = A\_i |\psi\rangle, then compute a kind of “mixed correlator” \langle\psi| B\_j C\_k |\psi'\_i\rangle for all j and k for a fixed i, then repeat for different values of i.

Our `correlation_matrix` function does not support putting different states around the operators, so you would have to also implement the two-point correlator part of that strategy above yourself. Hope that’s helpful to think about –

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**Author:** ![ZAHID-8017](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/zahid-8017/32/702_2.png) [@ZAHID-8017](https://itensor.discourse.group/u/ZAHID-8017)\
**Post date:** [February 18, 2025, 4:46am UTC](https://itensor.discourse.group/t/multi-point-correlation-function-using-itensor-dmrg/2238/5 "2025-02-18T04:46:46Z")

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Nice! Thanks for your response. Sure, I will try this strategy.

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**Author:** ![ZAHID-8017](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/zahid-8017/32/702_2.png) [@ZAHID-8017](https://itensor.discourse.group/u/ZAHID-8017)\
**Post date:** [March 24, 2025, 7:29am UTC](https://itensor.discourse.group/t/multi-point-correlation-function-using-itensor-dmrg/2238/6 "2025-03-24T07:29:09Z")

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![Multi_Point_Corr](https://global.discourse-cdn.com/free1/uploads/itensor/original/1X/ea19343810fab829f6954ecca102cdc1a7ac1ece.png)

Dear All, please find the attached png file, where I have structured my question using the latex format. I also want to know what the role of F\_{up}, and F\_{down} is?