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

General Discussion
1

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

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

pic2
pic21608×162 21 KB

pic3
pic31448×260 6.81 KB

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