Feature: more advanced mixing method for non-colinear calculations

[WHUweiqingzhou]

Background

Although mixing method for non-colinear calculations is more reliable and flexible after PR #3330, the convergence of non-colinear systems is still a difficult problem. Maybe we can try some new method, f. e. Journal of the Physical Society of Japan 82 (2013) 114706.

Describe the solution you'd like

Realize the mixing method for non-colinear calculations purposed by Journal of the Physical Society of Japan 82 (2013) 114706.

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.