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

Christopher L. Baldwin

doi:10.1103/PhysRevB.111.184204

paper

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

arXiv:2409.17242 · doi:10.1103/PhysRevB.111.184204

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 $h^{- α}$ , it is impossible for any operator evolving in the Heisenberg picture to spread with dynamical exponent less than $1/ α$ . In particular, ballistic growth is impossible for $α < 1$ , diffusive growth is impossible for $α < 1/2$ , and any finite dynamical exponent becomes impossible for sufficiently small $α$ . 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.

Published version (very minor updates following comments from colleagues and reviewers)

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