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

Martin Gebert; Bruno Nachtergaele; Jake Reschke; Robert Sims

doi:10.1007/s00023-020-00959-5

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

Martin Gebert, Bruno Nachtergaele, Jake Reschke, Robert Sims

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We introduce a class of UV-regularized two-body interactions for fermions in 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 Schrödinger 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.

Original language	English (US)
Pages (from-to)	3609-3637
Number of pages	29
Journal	Annales Henri Poincare
Volume	21
Issue number	11
DOIs	https://doi.org/10.1007/s00023-020-00959-5
State	Published - Nov 1 2020

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Nuclear and High Energy Physics
Mathematical Physics

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abstract = "We introduce a class of UV-regularized two-body interactions for fermions in Rd 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{\"o}dinger 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.",

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AU - Sims, Robert

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AB - We introduce a class of UV-regularized two-body interactions for fermions in Rd 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 Schrödinger 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.

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

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