Tightening the Lieb-Robinson bound in locally-interacting systems

In a recent work [1] we have shown that the finite-size error of numerical simulations of many-body quantum dynamics can be bounded using Lieb-Robinson bounds. However, while quantitative accuracy of the LR bounds is crucial for this application and others, previous LR bounds are usually extremely loose. In this talk we present a method [2] that dramatically and qualitatively improves LR bounds in systems with finite-range interactions. In prototypical models such as spin-1/2 Ising and Fermi-Hubbard models, our method improves the LR velocity by an order of magnitude with typical model parameters. More prominently, in systems with a large local Hilbert space dimension D, our method gives a LR velocity that grows much slower than previous bounds as D becomes large. For example, in the large-spin limits of the Heisenberg model and Wen's quantum rotor model and the large-number-of-orbitals limit of Hubbard models, our method gives a finite LR speed while all previous bounds diverge.

References:
[1] Z. Wang, M. Foss-Feig, and K. R. A. Hazzard, arXiv:2009.12032
[2] Z. Wang and K. R. A. Hazzard, PRX Quantum 1 (1), 010303 (2020)