A question about the ground state wave function of XXZ model

[EnigmaYu]

XXZ model in 1-dimension, with external field, what is the exact form of its ground state wave function? Recently I've read the ground state wave function of XY model and was curious about the condition of XXZ. Do they have a similar manner?
The XY result is attached below.

Thanks.

 

[Gec]

1D XY model with external field is equivalent to free fermions model. Because of this the ground state wave function has simple form. XXZ model can't be reduced to free fermions. Eigenfunctions of XXZ model have the form of Bethe ansatz. If external field is present, it is unknown what function from Bethe ansatz is the ground state wave function.

 

[charng]

Thank you for your question. The exact form of the ground state wave function for the XXZ model in 1-dimension with an external field is not currently known. There have been various theoretical and computational studies on the ground state properties of the XXZ model, but a closed-form expression for the ground state wave function has not been derived.

As for your question about the similarity between the XXZ and XY models, they do have some similarities in terms of their ground state properties. Both models exhibit quantum phase transitions, where the ground state changes from a magnetically ordered state to a disordered state as certain parameters are varied. However, the precise form of the ground state wave function may differ between the two models due to the different symmetries and interactions involved.

I have attached an image of the ground state wave function for the XY model for reference. Please note that this is just an example and the ground state wave function for the XXZ model may have a different form. I hope this helps answer your question.