Sub-ballistic operator growth in spin chains with heavy-tailed random fields

• URL: http://arxiv.org/abs/2409.17242v2
• Date: Mon, 28 Jul 2025 18:00:07 GMT
• Title: Sub-ballistic operator growth in spin chains with heavy-tailed random fields
• Abstract summary: We prove that it is impossible for any operator evolving in the Heisenberg picture to spread with dynamical exponent less than $1/alpha$.<n>This result establishes a wide family of models in which the disorder provably prevents conventional transport.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We rigorously prove that in nearly arbitrary quantum spin chains with power-law-distributed random fields, namely such that the probability of a field exceeding $h$ scales as $h^{-\alpha}$, it is impossible for any operator evolving in the Heisenberg picture to spread with dynamical exponent less than $1/\alpha$. In particular, ballistic growth is impossible for $\alpha < 1$, diffusive growth is impossible for $\alpha < 1/2$, and any finite dynamical exponent becomes impossible for sufficiently small $\alpha$. This result thus establishes a wide family of models in which the disorder provably prevents conventional transport. We express the result as a tightening of Lieb-Robinson bounds due to random fields -- the proof modifies the standard derivation such that strong fields appear as effective weak interactions, and then makes use of analogous recent results for random-bond spin chains.

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