Quantum States Reveal How Disorder Halts Energy Spread Within Materials

Key Takeaways

• Krylov complexity linearly scales with system size in ergodic phase
• Sublinear scaling indicates many-body localization and restricted state spread
• Method works for larger spin chains than entanglement entropy
• Krylov approach offers computationally efficient probe of quantum dynamics
• Potential to guide design of stable quantum devices

Pulse Analysis

The boundary between ergodic and many‑body‑localized (MBL) phases is a central problem in condensed‑matter physics. Ergodic systems rapidly scramble information, allowing thermalization, while MBL systems preserve memory of their initial state because disorder blocks energy transport. Traditional diagnostics such as entanglement entropy or level‑statistics become computationally infeasible as the number of spins exceeds a few dozen. Consequently, a scalable, sensitive probe is needed to study larger quantum devices and to guide the development of disorder‑tolerant technologies.

The authors introduce a Krylov‑space framework that builds a basis by repeatedly applying the Hamiltonian to an initial state, forming a ‘Krylov chain’. Krylov‑spread complexity measures how far the wavefunction extends within this chain. In the ergodic regime, complexity scales linearly with the Fock‑space dimension, meaning the state occupies a sizable fraction of the basis. In the MBL regime, growth is sublinear and amplitudes decay stretched‑exponentially, reflecting confinement to a tiny portion of the space. This approach avoids full wavefunction reconstruction, enabling analysis of much larger spin chains.

For quantum‑hardware designers, a fast indicator of delocalization versus localization can shape error‑correction protocols and material choices for qubits. Even slight disorder can erode coherence, so a low‑overhead metric like Krylov complexity could be integrated into the design workflow for superconducting, trapped‑ion, or topological platforms. Ongoing research aims to extend the method to higher‑dimensional lattices and long‑range interacting systems, potentially offering a universal diagnostic for emerging quantum simulators. Bridging theoretical insight with practical tools accelerates the path toward robust, scalable quantum technologies.