Optimal Frobenius light cone in spin chains with power-law interactions

Abstract

In many-body quantum systems with spatially local interactions, quantum information propagates with a finite velocity, reminiscent of the ``light cone" of relativity. In systems with long-range interactions which decay with distance $r$ as $1/r^{\alpha }$, however, there are multiple light cones which control different information theoretic tasks. We show an optimal (up to logarithms) ``Frobenius light cone" obeying $t\sim r^{\min (\alpha -1,1)}$ for $\alpha >1$ in one-dimensional power-law interacting systems with finite local dimension: this controls, among other physical properties, the butterfly velocity characterizing many-body chaos and operator growth. We construct an explicit random Hamiltonian protocol that saturates the bound and settles the optimal Frobenius light cone in one dimension. We partially extend our constraints on the Frobenius light cone to a several operator $p$-norms, and show that Lieb-Robinson bounds can be saturated in at most an exponentially small $e^{-\Omega (r)}$ fraction of the many-body Hilbert space.

17+20 pages, 3+1 figures. v2: expanded and published version

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• Optimal light cone for macroscopic particle transport in long-range systems: A quantum speed limit approach
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• Time optimal quantum state transfer in a fully-connected quantum computer
• From Light-Cone to Supersonic Propagation of Correlations by Competing Short- and Long-Range Couplings
• Lieb-Robinson correlation function for the quantum transverse field Ising model
• Frobenius light cone and the shift unitary
• Clustering of steady-state correlations in open systems with long-range interactions
• Revealing effects of local dimension on variable-range interacting model by connecting Lieb-Robinson bounds and multipartite entanglement
• Floquet thermalization by power-law induced permutation symmetry breaking