SKM 2023 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 64: Topology: Other Topics
TT 64.4: Vortrag
Freitag, 31. März 2023, 10:15–10:30, HSZ 201
Topological classification of single-particle Green functions and effective Hamiltonians for interacting systems — Maximilian Kotz1 and •Carsten Timm1,2 — 1Institute of Theoretical Physics, TU Dresden, 01062 Dresden, Germany — 2Würzburg-Dresden Cluster of Excellence ct.qmat, TU Dresden, 01062 Dresden, Germany
The single-particle Green function for any interacting-electron system can be written as the resolvent of a generally frequency-dependent and non-Hermitian effective Hamiltonian. Both these properties together allow for 54 instead of ten global-symmetry classes. The absence of Hermiticity also requires to reconsider the concept of a spectral gap. If the limits of the effective Hamiltonian for frequency ω → ±∞ coincide one can compactify the frequency axis and consider winding in (d+1)-dimensional momentum-frequency space. We derive a complete list of the homotopy groups for the 54 classes and spatial dimensions d, for the cases without and with frequency dependence.