Krylov Delocalization/Localization across Ergodicity Breaking

Autor:	Menzler, Heiko Georg, Jha, Rishabh
Rok vydání:	2024
Předmět:	Quantum Physics Condensed Matter - Disordered Systems and Neural Networks Condensed Matter - Strongly Correlated Electrons High Energy Physics - Theory
Zdroj:	Phys. Rev. B 110, 125137 (2024)
Druh dokumentu:	Working Paper
DOI:	10.1103/PhysRevB.110.125137
Popis:	Krylov complexity has recently gained attention where the growth of operator complexity in time is measured in terms of the off-diagonal operator Lanczos coefficients. The operator Lanczos algorithm reduces the problem of complexity growth to a single-particle semi-infinite tight-binding chain (known as the Krylov chain). Employing the phenomenon of Anderson localization, we propose the phenomenology of inverse localization length on the Krylov chain that undergoes delocalization/localization transition on the Krylov chain while the physical system undergoes ergodicity breaking. On the Krylov chain we find delocalization in an ergodic regime, as we show for the SYK model, and localization in case of a weakly ergodicity-broken regime. Considering the dynamics beyond scrambling, we find a collapse across different operators in the ergodic regime. We test for two settings: (1) the coupled SYK model, and (2) the quantum East model. Our findings open avenues for mapping ergodicity/weak ergodicity-breaking transitions to delocalization/localization phenomenology on the Krylov chain. Comment: 20 pages, 13 figures, published version
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.14384 Zobrazit plný text záznamu View this record from Arxiv