On Lieb-Robinson bounds for a class of continuum fermions

Abstract

We consider the quantum dynamics of a many-fermion system in ${\mathbb{R}}^d$ with an ultraviolet regularized pair interaction as previously studied in [M. Gebert, B. Nachtergaele, J. Reschke, and R. Sims, Ann. Henri Poincaré 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.

27 pages, 2 figures; v1->v2: added missing assumption in Corollaries 2.8 and 2.9

References in corpus (9)

• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Propagation of Correlations in Quantum Lattice Systems
• Speed limits and locality in many-body quantum dynamics
• Quantum Dynamics of Periodic and Limit-Periodic Jacobi and Block Jacobi Matrices with Applications to Some Quantum Many Body Problems
• Maximal speed for macroscopic particle transport in the Bose-Hubbard model
• On Lieb-Robinson bounds for the Bose-Hubbard model
• New Anomalous Lieb-Robinson Bounds in Quasi-Periodic XY Chains
• Maximal Speed of Propagation in Open Quantum Systems

Cited by in corpus (2)

• Quantum speedup from nonclassical polarization
• On the thermodynamic limit of interacting fermions in the continuum