Exponential bound on information spreading induced by quantum many-body dynamics with long-range interactions

Abstract

The dynamics of quantum systems strongly depends on the local structure of the Hamiltonian. For short-range interacting systems, the well-known Lieb-Robinson bound defines the effective light cone with an exponentially small error with respect to the spatial distance, whereas we can obtain only polynomially small error for distance in long-range interacting systems. In this paper, we derive a qualitatively new bound for quantum dynamics by considering how many spins can correlate with each other after time evolution. Our bound characterizes the number of spins which support the many-body entanglement with exponentially small error and is valid for large class of Hamiltonians including long-range interacting systems. To demonstrate the advantage of our approach in quantum many-body systems, we apply our bound to prove several fundamental properties which have not be derived from the Lieb-Robinson bound.

20 pages, 2 figures

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Cited by in corpus (13)

• Strictly linear light cones in long-range interacting systems of arbitrary dimensions
• Clustering of conditional mutual information for quantum Gibbs states above a threshold temperature
• Long-range topological insulators and weakened bulk-boundary correspondence
• Absence of fast scrambling in thermodynamically stable long-range interacting systems
• Effective Theory and Breakdown of Conformal Symmetry in a Long-Range Quantum Chain
• Spreading of correlations in exactly-solvable quantum models with long-range interactions in arbitrary dimensions
• Lieb-Robinson bound and almost-linear light-cone in interacting boson systems
• Singular dynamics and emergence of nonlocality in long-range quantum models
• Effective light cone and digital quantum simulation of interacting bosons
• Connecting probability distributions of different operators and generalization of the Chernoff-Hoeffding inequality
• Provably Efficient Simulation of 1D Long-Range Interacting Systems at Any Temperature
• Energy diffusion in the long-range interacting spin systems
• Entanglement area law and Lieb-Schultz-Mattis theorem in long-range interacting systems, and symmetry-enforced long-range entanglement