# How closely/exactly we can model the quasi 1D spin chain compound using the corresponding 1D spin chain model (effective hamiltonian) for it?

**URL:** <https://itensor.discourse.group/t/how-closely-exactly-we-can-model-the-quasi-1d-spin-chain-compound-using-the-corresponding-1d-spin-chain-model-effective-hamiltonian-for-it/1132>\
**Category:** General Discussion\
**Created:** [September 1, 2023, 4:36pm UTC](https://itensor.discourse.group/t/how-closely-exactly-we-can-model-the-quasi-1d-spin-chain-compound-using-the-corresponding-1d-spin-chain-model-effective-hamiltonian-for-it/1132 "2023-09-01T16:36:56Z")\
**Posts on this page:** 1\
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**Author:** ![Explorer](https://avatars.discourse-cdn.com/v4/letter/e/9d8465/32.png) [@Explorer](https://itensor.discourse.group/u/Explorer)\
**Post date:** [September 1, 2023, 4:36pm UTC](https://itensor.discourse.group/t/how-closely-exactly-we-can-model-the-quasi-1d-spin-chain-compound-using-the-corresponding-1d-spin-chain-model-effective-hamiltonian-for-it/1132/1 "2023-09-01T16:36:56Z")

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This ques might not fit to ‘itensor’, but it is an important question needs to be addressed.

I was wondering how closely we can write/model the 1D (lets say ) spin chain hamiltonian corresponding to quasi 1D spin chain compound.

Lets see the crystal structure of a quasi 1D trimerized Heisenberg spin 1 chain compound CaNi3P4O14, where trimers are formed by Ni atoms.

![pic](https://global.discourse-cdn.com/free1/uploads/itensor/original/1X/e8d29aaac1f4cc23ac4b83568b8c34330735be8e.png)

By seeing the crystal structure we can write the trimer spin hamitonian as:

 ![pic2](https://global.discourse-cdn.com/free1/uploads/itensor/original/1X/dce060537a8a4855a46007a289b450630169016c.png)  
 ![pic3](https://global.discourse-cdn.com/free1/uploads/itensor/original/1X/b47d616cc5e9995da78eb591607d886d723c8d24.png)

Here only three information about the compound is going into the model:  
(1) Trimer Structure of spin chain  
(2) Magnetic Exchange parameter for the compound CaNi3P4O14.  
(3) Type and Magnitude of spin : Heisenberg, Spin =1 .

Moreover, here, we are considering the linear trimer spin chain in hamiltonain, but in compound CaNi3P4O14, trimer chains are at some angle to each other, will that matter ? **This is in contrast to DFT calculation where we consider the exact unit cell.**

Is this all about modeling the quasi 1D spin chain compound ? If not,

**then what is recipe to model the quasi 1D spin chain compounds using spin chain models**

**or how to write the effective Quantum spin chain Hamiltonian corresponding to the spin chain compound and how closely ?**

Detailed discussion on this will help many beginner in this field.  
Also reference in this direction will be very much helpful.

Thanks