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Krylov complexity in Lifshitz-type Dirac field theories.

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Title: Krylov complexity in Lifshitz-type Dirac field theories.
Authors: Imani, Hamid R.1 (AUTHOR) hamidrezaimani@webmail.guilan.ac.ir, Velni, Komeil Babaei1 (AUTHOR) babaeivelni@guilan.ac.ir, Mozaffar, M. Reza Mohammadi1 (AUTHOR) mmohammadi@guilan.ac.ir
Source: European Physical Journal C -- Particles & Fields. Sep2025, Vol. 85 Issue 9, p1-17. 17p.
Subjects: Lanczos method, Quantum field theory, Operator product expansions
Abstract: We study Krylov complexity in Lifshitz-type Dirac field theories with a generic dynamical critical exponent z. By computing the Lanczos coefficients for massless and massive cases, we analyze the growth and saturation behavior of Krylov complexity in different regimes. We incorporate a hard UV cutoff and investigate the effects of lattice discretization, revealing fundamental differences between continuum and lattice models. In the presence of a UV cutoff, Krylov complexity exhibits an initial exponential growth followed by a linear regime, with saturation values dictated by the cutoff scale. For the lattice model, we find a fundamental departure from the continuum case: due to the finite Krylov basis, Krylov complexity saturates rather than growing indefinitely. Our findings suggest that Lifshitz scaling influences operator growth and information spreading in quantum systems. We further find that increasing the Lifshitz exponent z suppresses Krylov complexity, entropy, and Lanczos growth in both massless and massive cases, while enhancing K-variance. This trend reverses under a hard UV cutoff, where complexity and entropy increase with z. In lattice models, early-time complexity and b n decay shift with z, echoing the continuum behavior of massive and massless regimes. [ABSTRACT FROM AUTHOR]
Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="AR" term="%22Imani%2C+Hamid+R%2E%22">Imani, Hamid R.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> hamidrezaimani@webmail.guilan.ac.ir</i><br /><searchLink fieldCode="AR" term="%22Velni%2C+Komeil+Babaei%22">Velni, Komeil Babaei</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> babaeivelni@guilan.ac.ir</i><br /><searchLink fieldCode="AR" term="%22Mozaffar%2C+M%2E+Reza+Mohammadi%22">Mozaffar, M. Reza Mohammadi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mmohammadi@guilan.ac.ir</i>
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  Data: <searchLink fieldCode="JN" term="%22European+Physical+Journal+C+--+Particles+%26+Fields%22">European Physical Journal C -- Particles & Fields</searchLink>. Sep2025, Vol. 85 Issue 9, p1-17. 17p.
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  Data: <searchLink fieldCode="DE" term="%22Lanczos+method%22">Lanczos method</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+field+theory%22">Quantum field theory</searchLink><br /><searchLink fieldCode="DE" term="%22Operator+product+expansions%22">Operator product expansions</searchLink>
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  Data: We study Krylov complexity in Lifshitz-type Dirac field theories with a generic dynamical critical exponent z. By computing the Lanczos coefficients for massless and massive cases, we analyze the growth and saturation behavior of Krylov complexity in different regimes. We incorporate a hard UV cutoff and investigate the effects of lattice discretization, revealing fundamental differences between continuum and lattice models. In the presence of a UV cutoff, Krylov complexity exhibits an initial exponential growth followed by a linear regime, with saturation values dictated by the cutoff scale. For the lattice model, we find a fundamental departure from the continuum case: due to the finite Krylov basis, Krylov complexity saturates rather than growing indefinitely. Our findings suggest that Lifshitz scaling influences operator growth and information spreading in quantum systems. We further find that increasing the Lifshitz exponent z suppresses Krylov complexity, entropy, and Lanczos growth in both massless and massive cases, while enhancing K-variance. This trend reverses under a hard UV cutoff, where complexity and entropy increase with z. In lattice models, early-time complexity and b n decay shift with z, echoing the continuum behavior of massive and massless regimes. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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              Text: Sep2025
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