Tightening the Lieb-Robinson Bound in Locally-Interacting Systems

Abstract

The Lieb-Robinson (LR) bound rigorously shows that in quantum systems with short-range interactions, the maximum amount of information that travels beyond an effective "light cone" decays exponentially with distance from the light-cone front, which expands at finite velocity. Despite being a fundamental result, existing bounds are often extremely loose, limiting their applications. We introduce a method that dramatically and qualitatively improves LR bounds in models with finite-range interactions. Most prominently, in systems with a large local Hilbert space dimension $D$, our method gives an LR velocity that grows much slower than previous bounds with $D$ as $D\to \infty$. For example, in the Heisenberg model with spin $S$, we find $v\le$ const. compared to the previous $v\propto S$ which diverges at large $S$, and in multiorbital Hubbard models with $N$ orbitals, we find $v\propto \sqrt{N}$ instead of previous $v\propto N$, and similarly in the $N$-state truncated Bose-Hubbard model and Wen's quantum rotor model. Our bounds also scale qualitatively better in some systems when the spatial dimension or certain model parameters become large, for example in the $d$-dimensional quantum Ising model and perturbed toric code models. Even in spin-1/2 Ising and Fermi-Hubbard models, our method improves the LR velocity by an order of magnitude with typical model parameters, and significantly improves the LR bound at large distance and early time.

23 pages, 8 figures

References in corpus (21)

• 14-qubit entanglement: creation and coherence
• Local stabilizer codes in three dimensions without string logical operators
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Quantum Communication through Spin Chain Dynamics: an Introductory Overview
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Nearly-linear light cones in long-range interacting quantum systems
• General entanglement scaling laws from time evolution
• Entropy and Entanglement in Quantum Ground States
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
• Finite speed of quantum scrambling with long range interactions
• Strictly linear light cones in long-range interacting systems of arbitrary dimensions
• Quantum correlations and entanglement in far-from-equilibrium spin systems
• Spectral weight redistribution in strongly correlated bosons in optical lattices
• A Multi-Dimensional Lieb-Schultz-Mattis Theorem
• Signaling and Scrambling with Strongly Long-Range Interactions
• Lieb-Robinson bounds and the speed of light from topological order
• Lieb-Robinson bounds for open quantum systems with long-ranged interactions
• New Anomalous Lieb-Robinson Bounds in Quasi-Periodic XY Chains
• The ground state of a class of noncritical 1D quantum spin systems can be approximated efficiently
• Time-Polynomial Lieb-Robinson bounds for finite-range spin-network models

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