Speed limits to the growth of Krylov complexity in open quantum systems

Aranya Bhattacharya; Pingal Pratyush Nath; Himanshu Sahu

doi:10.1103/PhysRevD.109.L121902

Speed limits to the growth of Krylov complexity in open quantum systems

Aranya Bhattacharya, Pingal Pratyush Nath, Himanshu Sahu

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

9 Citations (Scopus)

Abstract

Recently, the propagation of information through quantum many-body systems, developed to study quantum chaos, have found many applications from black holes to disordered spin systems. Among other quantitative tools, Krylov complexity has been explored as a diagnostic tool for information scrambling in quantum many-body systems. We introduce a universal limit to the growth of the Krylov complexity in dissipative open quantum systems by utilizing the uncertainty relation for non-Hermitian operators. We also present the analytical results of Krylov complexity for characteristic behavior of Lanczos coefficients in dissipative systems. The validity of these results is demonstrated by explicit study of transverse-field Ising model under dissipative effects.

Original language	English
Article number	L121902
Number of pages	6
Journal	Phys. Rev. D
Volume	109
Issue number	12
DOIs	https://doi.org/10.1103/PhysRevD.109.L121902
Publication status	Published - 12 Jun 2024

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Publisher Copyright:
© 2024 American Physical Society.

Keywords

quant-ph
hep-th

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10.1103/PhysRevD.109.L121902

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abstract = "Recently, the propagation of information through quantum many-body systems, developed to study quantum chaos, have found many applications from black holes to disordered spin systems. Among other quantitative tools, Krylov complexity has been explored as a diagnostic tool for information scrambling in quantum many-body systems. We introduce a universal limit to the growth of the Krylov complexity in dissipative open quantum systems by utilizing the uncertainty relation for non-Hermitian operators. We also present the analytical results of Krylov complexity for characteristic behavior of Lanczos coefficients in dissipative systems. The validity of these results is demonstrated by explicit study of transverse-field Ising model under dissipative effects.",

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AU - Bhattacharya, Aranya

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AU - Sahu, Himanshu

PY - 2024/6/12

Y1 - 2024/6/12

N2 - Recently, the propagation of information through quantum many-body systems, developed to study quantum chaos, have found many applications from black holes to disordered spin systems. Among other quantitative tools, Krylov complexity has been explored as a diagnostic tool for information scrambling in quantum many-body systems. We introduce a universal limit to the growth of the Krylov complexity in dissipative open quantum systems by utilizing the uncertainty relation for non-Hermitian operators. We also present the analytical results of Krylov complexity for characteristic behavior of Lanczos coefficients in dissipative systems. The validity of these results is demonstrated by explicit study of transverse-field Ising model under dissipative effects.

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JF - Phys. Rev. D

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ER -

Speed limits to the growth of Krylov complexity in open quantum systems

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