Krylov complexity for non-local spin chains

TL;DR

This paper explores how non-local interactions in spin chains influence operator growth and quantum chaos, revealing faster information scrambling and nuanced distinctions in complexity saturation and growth.

Contribution

It introduces the use of Krylov complexity to analyze non-local spin chains, highlighting how non-locality affects operator growth and chaos indicators.

Findings

Non-locality accelerates operator scrambling.

Saturation values of Krylov complexity are less distinct in non-local regimes.

Early time complexity growth differentiates degrees of non-locality.

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.