Request for non-collinear functional needed in gks and spin spiral calculation( directly setting q vector)

[YuleZhang936]

Background

If abacus wants to handle non-collinear magnetism, generalized kohn-sham is needed. Thus, non-collinear functional is needed since gks needs noncollinear functional. A good application for non-collinear functional is spin spiral material.

Describe the solution you'd like

Here is a numerically stable option for non-collinear functional. To the best of what we know, it is the only one. We hope that abacus can have this non-collinear functional approach called the multi-collinear approach.
Ref: PHYSICAL REVIEW RESEARCH 5, 013036 (2023)

Task list only for developers

• Notice possible changes of behavior
• Explain the changes of codes in core modules of ESolver, HSolver, ElecState, Hamilt, Operator or Psi

Notice Possible Changes of Behavior (Reminder only for developers)

No response

Notice any changes of core modules (Reminder only for developers)

No response

Notice Possible Changes of Core Modules (Reminder only for developers)

No response

Additional Context

No response

Task list for Issue attackers (only for developers)

• Review and understand the proposed feature and its importance.
• Research on the existing solutions and relevant research articles/resources.
• Discuss with the team to evaluate the feasibility of implementing the feature.
• Create a design document outlining the proposed solution and implementation details.
• Get feedback from the team on the design document.
• Develop the feature following the agreed design.
• Write unit tests and integration tests for the feature.
• Update the documentation to include the new feature.
• Perform code review and address any issues.
• Merge the feature into the main branch.
• Monitor for any issues or bugs reported by users after the feature is released.
• Address any issues or bugs reported by users and continuously improve the feature.