# Nearest neighbour spin-spin correlation in 1D Heisenberg Model

**URL:** <https://itensor.discourse.group/t/nearest-neighbour-spin-spin-correlation-in-1d-heisenberg-model/2128>\
**Category:** DMRG and Numerical Methods\
**Created:** [November 14, 2024, 4:12pm UTC](https://itensor.discourse.group/t/nearest-neighbour-spin-spin-correlation-in-1d-heisenberg-model/2128 "2024-11-14T16:12:12Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![Jyoti\_Bisht](https://avatars.discourse-cdn.com/v4/letter/j/8baadc/32.png) [@Jyoti\_Bisht](https://itensor.discourse.group/u/Jyoti_Bisht)\
**Post date:** [November 14, 2024, 4:12pm UTC](https://itensor.discourse.group/t/nearest-neighbour-spin-spin-correlation-in-1d-heisenberg-model/2128/1 "2024-11-14T16:12:12Z")

</div>

When I find out spin-spin correlation i.e. \<S\_i.S\_{i+1}\>(nearest-neighbour), even for large system size it shows an oscillatory behaviour. Though it is oscillating around the correct value which is “-0.44314”, but shouldn’t it show a constant value in the bulk?? Because this behaviour even for large system size leads to a false dimerization in the bulk.

 ![HeisenbergL500](https://global.discourse-cdn.com/free1/uploads/itensor/original/1X/4336f97cb3dc57f2c6b86b0abb8d92136962cef1.jpeg)

---

<div class="post-metadata">

**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 14, 2024, 4:36pm UTC](https://itensor.discourse.group/t/nearest-neighbour-spin-spin-correlation-in-1d-heisenberg-model/2128/2 "2024-11-14T16:36:26Z")

</div>

What model is it (e.g. is it spin 1/2 or spin 1?) and how does the behavior change as you consider larger system sizes? If it’s the S=1/2 case, that is a gapless system so the edge effects may decay very slowly. Do your results change if you perform more DMRG sweeps and make the calculation more accurate?

---

<div class="post-metadata">

**Author:** ![Jyoti\_Bisht](https://avatars.discourse-cdn.com/v4/letter/j/8baadc/32.png) [@Jyoti\_Bisht](https://itensor.discourse.group/u/Jyoti_Bisht)\
**Post date:** [November 14, 2024, 4:49pm UTC](https://itensor.discourse.group/t/nearest-neighbour-spin-spin-correlation-in-1d-heisenberg-model/2128/3 "2024-11-14T16:49:27Z")

</div>

It is spin 1/2 case… Even if I increase the system size and sweeps the decay of these oscillations is very small.

---

<div class="post-metadata">

**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 14, 2024, 5:16pm UTC](https://itensor.discourse.group/t/nearest-neighbour-spin-spin-correlation-in-1d-heisenberg-model/2128/4 "2024-11-14T17:16:47Z")

</div>

I think this may just be the correct behavior of this system, due to the combination of open boundaries and the fact that it is a critical / gapless system. Does that answer your question about it?

---

<div class="post-metadata">

**Author:** ![Jyoti\_Bisht](https://avatars.discourse-cdn.com/v4/letter/j/8baadc/32.png) [@Jyoti\_Bisht](https://itensor.discourse.group/u/Jyoti_Bisht)\
**Post date:** [November 14, 2024, 6:04pm UTC](https://itensor.discourse.group/t/nearest-neighbour-spin-spin-correlation-in-1d-heisenberg-model/2128/5 "2024-11-14T18:04:36Z")

</div>

yes. I understand your point.

Thank you.