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  • Open Access

Lieb-Robinson correlation function for long disordered transverse-field Ising chains

Brendan J. Mahoney

Craig S. Lent*

  • Department of Electrical Engineering and Department of Physics and Astronomy, University of Notre Dame, Notre Dame, Indiana 46556, USA

  • *Contact author: lent@nd.edu
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Phys. Rev. Research 8, 033292 – Published 8 September, 2026

DOI: https://doi.org/10.1103/xd68-dpwm

Abstract

The Lieb-Robinson correlation function can be used to characterize the propagation of quantum information in Ising chains. Considerable work has been done to establish bounds on this correlation function in various circumstances. To actually calculate the value of the correlation function directly typically requires a state space that grows exponentially with system size, and so is intractable for all but relatively small systems. We employ a recently developed method that enables direct calculation of the Lieb-Robinson correlation function and that scales linearly with system size. This enables the computation for systems with more than a thousand qubits, revealing the propagation of quantum information down the chain. We extend this technique to the problem of Ising chains with randomly disordered coupling strengths. Increasing disorder causes localization of the quantum correlations and halts propagation of quantum information down the chain. We see light-cone isocontours therefore becoming vertical. The decay of correlations down the chain is characterized by a correlation length that in the paramagnetic phase increases quadratically with mean coupling strength and inverse quadratically with disorder level. The correlation length peaks at the phase transition. We map our general expression for the correlation function in the Ising system onto the probability density in the single-particle tight-binding Su-Schrieffer-Heeger model for a specific initial condition.

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Phys. Rev. Research 8, 033292– Published 8 September, 2026
  • Received 27 December 2025
  • Accepted 20 August 2026
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