München 2019 – wissenschaftliches Programm
PV VIII: Plenarvortrag
Mittwoch, 20. März 2019, 09:15–10:00, Plenarsaal
Particle-hole symmetries in condensed matter — •Martin Zirnbauer — University of Cologne, Koeln, Germany
Non-relativistic condensed matter breaks the charge conjugation symmetry C of relativistic quantum fields. However, for half-filled bands a close analog, namely particle-hole symmetry C', may emerge. The two symmetry operations C and C' are similar in that they both transform any excitation of energy E and charge Q to another excitation of the same energy E but the opposite charge -Q. They differ in that charge conjugation is a unitary operation, whereas particle-hole conjugation is anti-unitary.
After reviewing some background material from many-body theory, this talk illustrates the phenomenon of emergent particle-hole symmetries in condensed matter by a series of examples, culminating with the spectacular case of the half-filled lowest Landau level. Along the way, we argue that the Nobel Prize winning Haldane phase of anti-ferromagnetic quantum spin chains is a topological phase protected by a particle-hole symmetry.