On Lieb-Robinson bounds for a class of continuum fermions
- URL: http://arxiv.org/abs/2310.17736v2
- Date: Fri, 10 Nov 2023 09:40:26 GMT
- Title: On Lieb-Robinson bounds for a class of continuum fermions
- Authors: Benjamin Hinrichs, Marius Lemm, Oliver Siebert
- Abstract summary: We consider the quantum dynamics of a many-fermion system in $mathbb Rd$ with an ultraviolet regularized pair interaction.
We develop a fermionic continuum notion of conditional expectation and use it to approximate time-evolved fermionic observables by local ones.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We consider the quantum dynamics of a many-fermion system in $\mathbb R^d$
with an ultraviolet regularized pair interaction as previously studied in [M.
Gebert, B. Nachtergaele, J. Reschke, and R. Sims, Ann. Henri Poincar\'e 21.11
(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 $L^2$-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.
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