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Lieb-Robinson bounds for a class of continuum fermions

Mathematical Physics Seminar

Speaker: Oliver Siebert, UC Davis
Location: 3024 QMAP
Start time: Mon, Feb 10 2025, 4:10PM

We establish a Lieb-Robinson bound for a d-dimensional continuous many-body fermionic system with an ultraviolet regularized pair interaction, as previously studied by M. Gebert, B. Nachtergaele, J. Reschke, and R. Sims. Our proof is based on the ASTLO method and works for a general class of potentials. Furthermore, we also improve the associated one-body Lieb-Robinson bound to an almost ballistic one (i.e., an almost linear light cone). Finally, we discuss several applications, including the existence of a strongly continuous infinite-volume dynamics on the CAR algebra, the clustering of ground states in the presence of a spectral gap, and a fermionic continuum notion of conditional expectation. This is joint work with B. Hinrichs and M. Lemm.