The Lieb-Robinson light cone for power-law interactions

Abstract

The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as $1/r^{\alpha }$ at distance $r$? Here, we present a definitive answer to this question for all exponents $\alpha >2d$ and all spatial dimensions $d$. Schematically, information takes time at least $r^{\min \{1,\alpha -2d\}}$ to propagate a distance~$r$. As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.

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Cited by in corpus (27)

• Bounds in Nonequilibrium Quantum Dynamics
• Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics
• Strong quantum metrological limit from many-body physics
• Measuring Arbitrary Physical Properties in Analog Quantum Simulation
• Topological Speed Limit
• Transport and entanglement growth in long-range random Clifford circuits
• Quantum many-body systems in thermal equilibrium
• Maximal speed for macroscopic particle transport in the Bose-Hubbard model
• Dynamical scaling of correlations generated by short- and long-range dissipation
• Finite speed of quantum information in models of interacting bosons at finite density
• Local variational quantum compilation of a large-scale Hamiltonian dynamics
• Long-Range Free Fermions: Lieb-Robinson Bound, Clustering Properties, and Topological Phases
• Optimal Frobenius light cone in spin chains with power-law interactions
• Generating long-lived entangled states with free-space collective spontaneous emission
• Entanglement Phases in large-N hybrid Brownian circuits with long-range couplings
• Exponential clustering of bipartite quantum entanglement at arbitrary temperatures
• Prethermalization and the local robustness of gapped systems
• Effective light cone and digital quantum simulation of interacting bosons
• Scaling laws for non-Hermitian skin effect with long-range couplings
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• Entanglement propagation and dynamics in non-additive quantum systems
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• Implementing a Fast Unbounded Quantum Fanout Gate Using Power-Law Interactions
• Photon-mediated interactions near a Dirac photonic crystal slab