Symmetry-adapted closest Wannier modeling based on complete multipole basis set (2501.10056v1)

Abstract: We have developed a method to construct a symmetry-adapted Wannier tight-binding model based on the closest Wannier formalism and the symmetry-adapted multipole theory. Since the symmetry properties of the closest Wannier functions are common to those of the original atomic orbitals, symmetry-adapted multipole basis (SAMB) can be defined as the complete orthonormal matrix basis set in the Hilbert space of the closest Wannier functions. Utilizing the completeness and orthonormality of SAMBs, the closest Wannier Hamiltonian can be expressed as a linear combination of SAMBs belonging to the identity irreducible representation, thereby fully restoring the symmetry of the system. Moreover, the linear coefficients of each SAMB (model parameters) related to crystalline electric fields, spin-orbit coupling, and electron hoppings are determined through simple matrix projection without any iterative procedure. Thus, this method allows us to unveil mutual interplay among hidden electronic multipole degrees of freedom in the Hamiltonian and numerically evaluate them. We demonstrate the effectiveness of our method by modeling monolayer graphene under a perpendicular electric field, highlighting its utility in symmetrizing the closest Wannier model, quantifying symmetry breaking, and predicting unusual responses. The method is implemented in the open-source Python library SymClosestWannier, with the codes available on GitHub (https://github.com/CMT-MU/SymClosestWannier).

• The paper introduces a symmetry-adapted Wannier modeling method that leverages a complete multipole basis to preserve system symmetry and correct degeneracy issues.
• The methodology employs non-iterative matrix projections to efficiently extract tight-binding parameters, significantly reducing computational overhead.
• Numerical tests on monolayer graphene under an electric field validate improved predictions of spin-orbit couplings and electronic interactions.

Symmetry-Adapted Closest Wannier Modeling

The paper "Symmetry-adapted closest Wannier modeling based on complete multipole basis set" by Oiwa et al. presents an advanced methodological framework for constructing tight-binding models using symmetry-adapted Wannier functions. This work integrates the closest Wannier formalism with the symmetry-adapted multipole theory to achieve symmetry-preserving tight-binding models, addressing key challenges in density-functional theory (DFT) computations of material properties.

Overview

Wannier functions are essential for describing electronic states in materials, especially in constructing tight-binding (TB) models that are instrumental for studying electronic band structures and various phenomena driven by electronic correlations. However, conventional Wannier functions often suffer from minor symmetry-breaking issues, such as small energy degeneracy lifting, which can hinder accurate predictions of material properties, particularly those sensitive to symmetry.

The proposed approach resolves these issues by employing a symmetry-adapted multipole basis set (SAMB) in the closest Wannier formalism framework. The SAMBs provide a complete, orthonormal set of matrix elements that retain the symmetry of the system, capturing the electronic multipole degrees of freedom. These SAMBs are classified based on inversion and time-reversal parities, facilitating comprehensive characterization within the Hilbert space defined by Wannier functions.

The key innovation lies in post-processing symmetrization, where the closest Wannier Hamiltonian is expressed as a linear combination of SAMBs confined to the identity irreducible representation, ensuring symmetry fidelity without iterative calculations. This methodology leads to improved computational efficiency and precision.

Numerical Results and Claims

The application of this method is demonstrated through the modeling of monolayer graphene under a perpendicular electric field. This demonstration highlights:

1. Symmetry Preservation: The method successfully corrects symmetry-breaking artifacts and restores energy degeneracies that are critical for characterizing electronic band structures, especially for phenomena like the Rashba and intrinsic spin-orbit couplings.
2. Computational Efficiency: The use of non-iterative matrix projections to determine model parameters significantly reduces computational overhead compared to conventional iterative fitting techniques.
3. Comprehensive Parameter Extraction: The method allows direct calculation of model parameters such as crystalline electric fields, spin-orbit couplings, and electron hopping terms, providing extensive insights into electronic interactions.
4. Predictive Capability: By using the SAMB framework, the method provides predictive insights into unconventional material responses, including potential exotic orderings and responses induced by multipole interactions.

Implications and Future Directions

This work has substantial implications for both theoretical and practical advancements in computational material science:

• Theoretical Insights: The detailed mapping of hidden electronic multipole interactions facilitates deeper understanding of complex electronic phenomena and the novel phases of matter.
• Practical Applications: Enhanced accuracy in TB modeling can lead to better predictions for material properties, thereby assisting in the design of novel materials with tailored properties.
• Future Developments: The framework can be extended to include two-body interactions and phonon dynamics, opening avenues for more comprehensive modeling of lattice-electron interactions and correlated electron systems.

This paper lays the groundwork for developing a robust approach to high-precision, symmetry-consistent modeling in solid-state physics, potentially guiding the future of electronic structure calculations and material discovery.