Multiseed Krylov complexity

TL;DR

This paper introduces a multiseed approach to Krylov complexity, using a collection of simple operators to reliably differentiate between integrable and chaotic quantum systems without fine-tuning.

Contribution

It proposes a novel multiseed Krylov complexity method that improves the distinction between integrable and chaotic dynamics in quantum systems.

Findings

Multiseed Krylov complexity reliably distinguishes integrable and chaotic Hamiltonians.

Using all simple operators as seeds enhances the robustness of complexity measures.

The approach does not require fine-tuning to differentiate dynamical regimes.

Abstract

Krylov complexity is an attractive measure for the rate at which quantum operators spread in the space of all possible operators under dynamical evolution. One expects that its late-time plateau would distinguish between integrable and chaotic dynamics, but its ability to do so depends precariously on the choice of the initial seed. We propose to apply such considerations not to a single operator, but simultaneously to a collection of initial seeds in the manner of the block-Lanczos algorithm. We furthermore suggest that this collection should comprise all simple (few-body) operators in the theory, which echoes the applications of Nielsen complexity to dynamical evolution. The resulting construction, unlike the conventional Krylov complexity, reliably distinguishes integrable and chaotic Hamiltonians without any need for fine-tuning.