Exact ballistic energy transport and emergent XXZ dynamics in an integrable three-state chain
Abstract
We investigate the coupling dependence of ballistic energy transport and the emergent spin dynamics in an integrable Hermitian three-state chain that connects a clock interaction to a highly degenerate flag limit. By constructing a regular R-matrix to establish a globally conserved energy current, we analytically evaluate its full variance to obtain the exact, strictly positive leading high-temperature coefficient of the thermal Drude weight and the ballistic growth rate of the energy-correlation second moment. In the strong-coupling limit, the degeneracy is lifted by virtual transitions of a delocalized third-color spectator state, which generates an effective spin-1/2 XXZ Hamiltonian with anisotropy Δ= −1/2 and fundamentally selects the all-active two-color sector as the true ground state. For periodic boundaries, this virtual spectator motion introduces a positive length-changing XXZ supercharge squared that, for L≥4, strictly annihilates all states within a finite, length-independent energy interval above the ground state. Consequently, we rigorously prove that the full periodic effective theory perfectly replicates the exact low-energy XXZ spectrum, including all state multiplicities, as well as its macroscopic bulk free-energy density.
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BibTeX
@misc{liang2026exact,
title = {{Exact ballistic energy transport and emergent XXZ dynamics in an integrable three-state chain}},
author = {Hanbing Liang and Fujun Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22817},
eprint = {2609.22817},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22817},
}
RIS
TY - UNPB
TI - Exact ballistic energy transport and emergent XXZ dynamics in an integrable three-state chain
AU - Hanbing Liang
AU - Fujun Liu
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.22817
UR - https://arxiv.org/abs/2609.22817
AB - We investigate the coupling dependence of ballistic energy transport and the emergent spin dynamics in an integrable Hermitian three-state chain that connects a clock interaction to a highly degenerate flag limit. By constructing a regular R-matrix to establish a globally conserved energy current, we analytically evaluate its full variance to obtain the exact, strictly positive leading high-temperature coefficient of the thermal Drude weight and the ballistic growth rate of the energy-correlation second moment. In the strong-coupling limit, the degeneracy is lifted by virtual transitions of a delocalized third-color spectator state, which generates an effective spin-1/2 XXZ Hamiltonian with anisotropy Δ= −1/2 and fundamentally selects the all-active two-color sector as the true ground state. For periodic boundaries, this virtual spectator motion introduces a positive length-changing XXZ supercharge squared that, for L≥4, strictly annihilates all states within a finite, length-independent energy interval above the ground state. Consequently, we rigorously prove that the full periodic effective theory perfectly replicates the exact low-energy XXZ spectrum, including all state multiplicities, as well as its macroscopic bulk free-energy density.
ER -