Regensburg 2019 – wissenschaftliches Programm

Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe

TT: Fachverband Tiefe Temperaturen

TT 68: Topology: Other Topics

TT 68.10: Vortrag

Freitag, 5. April 2019, 12:00–12:15, H22

Bulk-boundary correspondence for non-Hermitian Hamiltonians — •Heinrich-Gregor Zirnstein¹, Bernd Rosenow¹, and Gil Refael² — ¹Institut für Theoretische Physik, Universität Leipzig, Germany — ²Institute of Quantum Information and Matter, California Institute of Technology, USA

For sufficiently strong gain and loss, genuinely non-Hermitian topological phases can be realized and characterized by generalized topological invariants. In such phases, the Hamiltonian cannot be deformed into a gapped Hermitian Hamiltonian without the energy bands touching each other. Since the so-called non-Hermitian skin effect causes localization of all eigenstates at a boundary of the system, we discuss topological properties by focusing on response functions, which are experimental observables. In particular, a comparison of Green functions for periodic and open boundary conditions shows that in general there is no correspondence between topological invariants computed for periodic boundary conditions, and edge states observed for open boundary conditions. We prove these statements for one-dimensional systems in several symmetry classes, and discuss generalizations to higher spatial dimensions. In particular, in more than one spatial dimension, every Hamiltonian whose bands do not touch each other is topologically equivalent to a Hermitian one, and non-Hermitian topological indices are only possible when bands touch each other.