Discussion Overview
The discussion centers on the U(N) invariance of the Bloch ground state as mentioned in Hasan & Kane's review on topological insulators. Participants explore the implications of this invariance in the context of Hartree and Hartree Fock wavefunctions, as well as the relationship to Bloch functions and their transformation properties.
Discussion Character
- Technical explanation
- Conceptual clarification
- Debate/contested
Main Points Raised
- Jan questions the U(N) invariance of the Bloch ground state as stated in Hasan & Kane's review.
- One participant explains that Hartree and Hartree Fock wavefunctions are invariant under unitary transformations of occupied and unoccupied orbitals, suggesting that Bloch functions have special properties related to this invariance.
- A transformation to localized Wannier functions is mentioned as a popular unitary transformation related to Bloch functions.
- Another participant corrects the earlier mention of "Brillouin functions" to "Wannier functions" and references Roy McWeeny's book for further details on the invariance of many-particle wavefunctions.
- The invariance of determinants under unitary transformations is noted as a fundamental concept in this context.
Areas of Agreement / Disagreement
Participants express differing views on the clarity and implications of U(N) invariance in the context of Bloch ground states, indicating that the discussion remains unresolved regarding Jan's initial question.
Contextual Notes
There are references to specific transformations and concepts that may require further clarification, such as the distinction between Bloch and Wannier functions, and the foundational principles of linear algebra related to invariance.