On Lieb-Robinson Bounds for a Class of Continuum Fermions

Abstract We consider the quantum dynamics of a many-fermion system in $${{\mathbb {R}}}^d$$ R d with an ultraviolet regularized pair interaction as previously studied in Gebert et al. (Ann Henri Poincaré 21(11):3609–3637, 2020). We provide a Lieb–Robinson bound under substantially relaxed assumptions on the potentials. We also improve the associated one-body Lieb–Robinson bound on $$L^2$$ L 2 -overlaps to an almost ballistic one (i.e., an almost linear light cone) under the same relaxed assumptions. Applications include the existence of the infinite-volume dynamics and clustering of ground states in the presence of a spectral gap. We also develop a fermionic continuum notion of conditional expectation and use it to approximate time-evolved fermionic observables by local ones, which opens the door to other applications of the Lieb–Robinson bounds.

arXiv:2310.17736Annales Henri PoincaréJul 12, 20245 citations

Lieb–Robinson Bounds, Automorphic Equivalence and LPPL for Long-Range Interacting Fermions

Stefan Teufel, Tom Wessel

arXiv:2507.03319Mathematical Physics Analysis and GeometryOct 27, 20260 citations

On Lieb-Robinson Bounds for a Class of Continuum Fermions

Marius Lemm, Oliver Siebert

Published Jan 1, 2025• 0 citations

Publisher

DOI: 10.15496/publikation-122187

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Lieb–Robinson Bounds and Strongly Continuous Dynamics for a Class of Many-Body Fermion Systems in

{\mathbb {R}}^d

Abstract We consider the quantum dynamics of a many-fermion system in

{{\mathbb {R}}}^d

R d with an ultraviolet regularized pair interaction as previously studied in Gebert et al. (Ann Henri Poincaré 21(11):3609–3637, 2020). We provide a Lieb–Robinson bound under substantially relaxed assumptions on the potentials. We also improve the associated one-body Lieb–Robinson bound on

L^2

L 2 -overlaps to an almost ballistic one (i.e., an almost linear light cone) under the same relaxed assumptions. Applications include the existence of the infinite-volume dynamics and clustering of ground states in the presence of a spectral gap. We also develop a fermionic continuum notion of conditional expectation and use it to approximate time-evolved fermionic observables by local ones, which opens the door to other applications of the Lieb–Robinson bounds.