Related papers: Krylov Complexity in Open Quantum Systems

Krylov Complexity in Open Quantum Systems

URL: http://arxiv.org/abs/2207.13603v2
Date: Wed, 10 Aug 2022 18:02:53 GMT
Title: Krylov Complexity in Open Quantum Systems
Authors: Chang Liu, Haifeng Tang and Hui Zhai
Abstract summary: We show that Krylov complexity in open systems can be mapped to a non-hermitian tight-binding model in a half-infinite chain. Our work provides insights for discussing complexity, chaos, and holography for open quantum systems.
Score: 3.5895926924969404
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Krylov complexity is a novel measure of operator complexity that exhibits universal behavior and bounds a large class of other measures. In this letter, we generalize Krylov complexity from a closed system to an open system coupled to a Markovian bath, where Lindbladian evolution replaces Hamiltonian evolution. We show that Krylov complexity in open systems can be mapped to a non-hermitian tight-binding model in a half-infinite chain. We discuss the properties of the non-hermitian terms and show that the strengths of the non-hermitian terms increase linearly with the increase of the Krylov basis index $n$. Such a non-hermitian tight-binding model can exhibit localized edge modes that determine the long-time behavior of Krylov complexity. Hence, the growth of Krylov complexity is suppressed by dissipation, and at long-time, Krylov complexity saturates at a finite value much smaller than that of a closed system with the same Hamitonian. Our conclusions are supported by numerical results on several models, such as the Sachdev-Ye-Kitaev model and the interacting fermion model. Our work provides insights for discussing complexity, chaos, and holography for open quantum systems.

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