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Lieb-Robinson Bounds and the Exponential Clustering Theorem

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arxiv math-ph/0506030 v3 pith:WCTN332M submitted 2005-06-10 math-ph cond-mat.stat-mechmath.MP

classification math-phcond-mat.stat-mechmath.MP
keywords clusteringexponentiallieb-robinsonsystemsboundboundsclassdiscrete
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We give a Lieb-Robinson bound for the group velocity of a large class of discrete quantum systems which can be used to prove that a non-vanishing spectral gap implies exponential clustering in the ground state of such systems.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 415 citations worldwide. Full citation record

  1. Pure gapped ground states of spin chains are short-range entangled

    math-ph 2025-11 conditional novelty 8.0 of 10

    In one-dimensional finite-range spin chains, every pure gapped ground state is short-range entangled: an image of a product state under a locally generated automorphism with exponentially decaying tails.

  2. Noise structuring in fixed-depth Trotter simulation: stationary channels and observable-level depolarization

    quant-ph 2026-07 conditional novelty 6.0 of 10

    A fixed-depth Trotter protocol makes hardware noise almost endpoint-independent, producing a stationary binomial/Poisson noise channel and an observable-level affine contrast correction for error mitigation.

  3. Topological Control of Quantum Chaos Diagnostics: OTOCs, Spectral Statistics, and Information Scrambling in Ising Model

    quant-ph 2026-07 unverdicted novelty 5.0 of 10

    The study demonstrates that long-range couplings and heterogeneous degree distributions in Ising spin networks on path, Erdős–Rényi, and Watts–Strogatz topologies accelerate quantum information scrambling and chaos, d...

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