Workshop 2025: The geometry of the Hermitian matrix space and the Schrieffer-Wolff transformation

Session Information

Location: Lecture room Schay
Day: Friday, 16 May
Time: 09:30 - 10:00
Chairperson: Annika Johansson

Presentation Details

Presentation Type: Oral presentation
Title: The geometry of the Hermitian matrix space and the Schrieffer-Wolff transformation
Abstract: In quantum mechanics, the Schrieffer--Wolff (SW) transformation (also called quasi-degenerate perturbation theory) is known as an approximative method to reduce the dimension of the Hamiltonian. We present a geometric interpretation of the SW transformation: We prove that it induces a local coordinate chart in the space of Hermitian matrices near a k-fold degeneracy submanifold. Inspired by this result, we establish a `distance theorem': we show that the standard deviation of k neighboring eigenvalues of a Hamiltonian equals the distance of this Hamiltonian from the corresponding k-fold degeneracy submanifold, divided by √k. We show how these relations unify the phenomenology of protected spectral degeneracies in various subfields of physics, including Weyl semimetals, topological insulators and superconductors, and quantum error correction codes. Reference: G. Pinter, Gy. Frank, D. Varjas, A. Palyi, https://arxiv.org/abs/2407.10478

Presenter

Dr Andras Palyi
Budapest University of Technology and Economics | Hungary

Authors

1. Palyi, Andras | Department of Theoretical Physics, Budapest University of Technology and Economics