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arXiv · 2312.11677

Krylov complexity for non-local spin chains

Aranya Bhattacharya·Pingal Pratyush Nath·Himanshu Sahu
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Abstract

Building upon recent research in spin systems with non-local interactions, this study investigates operator growth using the Krylov complexity in different non-local versions of the Ising model. We find that the non-locality results in a faster scrambling of the operator to all sites. While the saturation value of Krylov complexity of local integrable and local chaotic theories differ by a significant margin, this difference is much suppressed when non-local terms are introduced in both regimes. This results from the faster scrambling of information in the presence of non-locality. In addition, we investigate the behavior of level statistics and spectral form factor as probes of quantum chaos to study the integrability breaking due to non-local interactions. Our numerics indicate that in the non-local case, late time saturation of Krylov complexity distinguishes between different underlying theories, while the early time complexity growth distinguishes different degrees of non-locality.

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Aranya Bhattacharya, Pingal Pratyush Nath, Himanshu Sahu. 2023-12-18. Krylov complexity for non-local spin chains. https://doi.org/10.1103/physrevd.109.066010

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