ePrints@IIScePrints@IISc Home | About | Browse | Latest Additions | Advanced Search | Contact | Help

On Krylov complexity in open systems: an approach via bi-Lanczos algorithm

Bhattacharya, A and Nandy, P and Nath, PP and Sahu, H (2023) On Krylov complexity in open systems: an approach via bi-Lanczos algorithm. In: Journal of High Energy Physics, 2023 (12).

[img]
Preview
PDF
jou_hig_ene_phy_2023_12_2023.pdf - Published Version

Download (1MB) | Preview
Official URL: https://doi.org/10.1007/JHEP12(2023)066

Abstract

Continuing the previous initiatives 1, 2, we pursue the exploration of operator growth and Krylov complexity in dissipative open quantum systems. In this paper, we resort to the bi-Lanczos algorithm generating two bi-orthogonal Krylov spaces, which individually generate non-orthogonal subspaces. Unlike the previously studied Arnoldi iteration, this algorithm renders the Lindbladian into a purely tridiagonal form, thus opening up a possibility to study a wide class of dissipative integrable and non-integrable systems by computing Krylov complexity at late times. Our study relies on two specific systems, the dissipative transverse-field Ising model (TFIM) and the dissipative interacting XXZ chain. We find that, for the weak coupling, initial Lanczos coefficients can efficiently distinguish integrable and chaotic evolution before the dissipative effect sets in, which results in more fluctuations in higher Lanczos coefficients. This results in the equal saturation of late-time complexity for both integrable and chaotic cases, making the notion of late-time chaos dubious. © 2023, The Author(s).

Item Type: Journal Article
Publication: Journal of High Energy Physics
Publisher: Springer Science and Business Media Deutschland GmbH
Additional Information: The copyright for this article belongs to authors.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Division of Physical & Mathematical Sciences > Instrumentation Appiled Physics
Date Deposited: 18 Nov 2024 21:07
Last Modified: 18 Nov 2024 21:07
URI: http://eprints.iisc.ac.in/id/eprint/85325

Actions (login required)

View Item View Item