Seeding and Amplification of Chaos in Long-Range Interacting Spin Chains
Abstract
Truncating weak interactions is a natural simplification of a many-body Hamiltonian, but the validity of this approximation need not be uniform in distance and time. In a chaotic system, a weak long-range coupling can seed a small disturbance far from its source, after which the local dynamics can amplify that disturbance exponentially. We study this mechanism in an infinite-temperature classical Heisenberg spin chain with a dominant nearest-neighbor exchange and a weak interaction tail. Using a classical decorrelator, we compare exponentially and power-law decaying tails over several decades in interaction strength. For exponentially decaying interactions, the long-distance front remains ballistic when the tail is sufficiently shallow, with a velocity controlled by the competition between the spatial decay of the seed and the local chaotic growth. For sufficiently rapid exponential decay, the nearest-neighbor front, which is defined by an intrinsic butterfly velocity vb, is recovered within the accessible space-time window. For power-law interactions, the arrival time is logarithmic in distance for all exponents studied, corresponding to an exponentially expanding spatial front; the power-law exponent controls the coefficient of this logarithm. We interpret both behaviors using a seeding-and-amplification picture in which long-range couplings generate weak disturbances throughout the chain whose growth is governed primarily by the local nearest-neighbor dynamics. In this picture, the overall strength of the tail primarily controls when the long-range front becomes visible, while its spatial decay controls the propagation law. Thus a weak interaction tail can leave conventional spin-dynamical observables essentially unchanged while qualitatively altering the long-distance propagation of decorrelation.
Related
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BibTeX
@misc{sabra2026seeding,
title = {{Seeding and Amplification of Chaos in Long-Range Interacting Spin Chains}},
author = {Sareen Sabra and Jeffrey G. Rau},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40417},
eprint = {2610.40417},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40417},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Seeding and Amplification of Chaos in Long-Range Interacting Spin Chains
AU - Sareen Sabra
AU - Jeffrey G. Rau
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40417
UR - https://arxiv.org/abs/2610.40417
AB - Truncating weak interactions is a natural simplification of a many-body Hamiltonian, but the validity of this approximation need not be uniform in distance and time. In a chaotic system, a weak long-range coupling can seed a small disturbance far from its source, after which the local dynamics can amplify that disturbance exponentially. We study this mechanism in an infinite-temperature classical Heisenberg spin chain with a dominant nearest-neighbor exchange and a weak interaction tail. Using a classical decorrelator, we compare exponentially and power-law decaying tails over several decades in interaction strength. For exponentially decaying interactions, the long-distance front remains ballistic when the tail is sufficiently shallow, with a velocity controlled by the competition between the spatial decay of the seed and the local chaotic growth. For sufficiently rapid exponential decay, the nearest-neighbor front, which is defined by an intrinsic butterfly velocity v_b, is recovered within the accessible space-time window. For power-law interactions, the arrival time is logarithmic in distance for all exponents studied, corresponding to an exponentially expanding spatial front; the power-law exponent controls the coefficient of this logarithm. We interpret both behaviors using a seeding-and-amplification picture in which long-range couplings generate weak disturbances throughout the chain whose growth is governed primarily by the local nearest-neighbor dynamics. In this picture, the overall strength of the tail primarily controls when the long-range front becomes visible, while its spatial decay controls the propagation law. Thus a weak interaction tail can leave conventional spin-dynamical observables essentially unchanged while qualitatively altering the long-distance propagation of decorrelation.
ER -