# Lieb–Robinson Bounds and Strongly Continuous Dynamics for a Class of Many-Body Fermion Systems in $${\mathbb {R}}^d$$

@article{Gebert2020LiebRobinsonBA, title={Lieb–Robinson Bounds and Strongly Continuous Dynamics for a Class of Many-Body Fermion Systems in \$\$\{\mathbb \{R\}\}^d\$\$}, author={Martin Gebert and Bruno Nachtergaele and Jake Reschke and Robert Sims}, journal={Annales Henri Poincar{\'e}}, year={2020} }

We introduce a class of UV-regularized two-body interactions for fermions in $\mathbb{R}^d$ and prove a Lieb-Robinson estimate for the dynamics of this class of many-body systems. As a step toward this result, we also prove a propagation bound of Lieb-Robinson type for Schr\"odinger operators. We apply the propagation bound to prove the existence of infinite-volume dynamics as a strongly continuous group of automorphisms on the CAR algebra.

## 6 Citations

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### On Lieb–Robinson Bounds for the Bose–Hubbard Model

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We consider the dynamics of the Bose–Hubbard model on general lattices and prove a Lieb–Robinson bound for observables whose supports are separated by an initially almost particle-free region. We…

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We extend Araki’s well-known results on the equivalence of the KMS condition and the variational principle for equilibrium states of quantum lattice systems with short-range interactions, to a large…

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