Breakdown of superdiffusion in perturbed quantum integrable spin chains and ladders
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915510110650368 |
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| author | Wang, Kevin Moore, Joel E. |
| author_facet | Wang, Kevin Moore, Joel E. |
| contents | Superdiffusive transport with dynamical exponent $z=3/2$ has been firmly established at finite temperature for a class of integrable systems with a non-abelian global symmetry $G$. On the inclusion of integrability-breaking perturbations, diffusive transport with $z=2$ is generically expected to hold in the limit of late time. Recent studies of the classical Haldane-Ishimori-Skylanin model have found that perturbations that preserve the global symmetry lead to a much slower timescale for the onset of diffusion, albeit with uncertainty over the exact scaling exponent. That is, for perturbations of strength $λ$, the characteristic timescale for diffusion goes as $t_*\sim λ^{-α}$ for some $α$. Using large-scale matrix product state simulations, we investigate this behavior for perturbations to the canonical quantum model showing superdiffusion: the $S=1/2$ quantum Heisenberg chain. We consider a ladder configuration and look at various perturbations that either break or preserve the $SU(2)$ symmetry, leading to scaling exponents consistent with those observed in one classical study arXiv:2402.18661: $α=2$ for symmetry-breaking terms and $α=6$ for symmetry-preserving terms. We also consider perturbations from another integrable point of the ladder model with $G=SU(4)$ and find consistent results. Finally, we consider a generalization to an $SU(3)$ ladder and find that the $α=6$ scaling appears to be universal across superdiffusive systems when the perturbations preserve the non-abelian symmetry $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08866 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Breakdown of superdiffusion in perturbed quantum integrable spin chains and ladders Wang, Kevin Moore, Joel E. Statistical Mechanics Superdiffusive transport with dynamical exponent $z=3/2$ has been firmly established at finite temperature for a class of integrable systems with a non-abelian global symmetry $G$. On the inclusion of integrability-breaking perturbations, diffusive transport with $z=2$ is generically expected to hold in the limit of late time. Recent studies of the classical Haldane-Ishimori-Skylanin model have found that perturbations that preserve the global symmetry lead to a much slower timescale for the onset of diffusion, albeit with uncertainty over the exact scaling exponent. That is, for perturbations of strength $λ$, the characteristic timescale for diffusion goes as $t_*\sim λ^{-α}$ for some $α$. Using large-scale matrix product state simulations, we investigate this behavior for perturbations to the canonical quantum model showing superdiffusion: the $S=1/2$ quantum Heisenberg chain. We consider a ladder configuration and look at various perturbations that either break or preserve the $SU(2)$ symmetry, leading to scaling exponents consistent with those observed in one classical study arXiv:2402.18661: $α=2$ for symmetry-breaking terms and $α=6$ for symmetry-preserving terms. We also consider perturbations from another integrable point of the ladder model with $G=SU(4)$ and find consistent results. Finally, we consider a generalization to an $SU(3)$ ladder and find that the $α=6$ scaling appears to be universal across superdiffusive systems when the perturbations preserve the non-abelian symmetry $G$. |
| title | Breakdown of superdiffusion in perturbed quantum integrable spin chains and ladders |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2501.08866 |