Krylov complexity in Lifshitz-type scalar field theories
Abstract We investigate various aspects of the Lanczos coefficients in a family of free Lifshitz scalar theories, characterized by their integer dynamical exponent, at finite temperature. In this non-relativistic setup, we examine the effects of mass, finite ultraviolet cutoff, and finite lattice sp...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-03-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-024-12609-9 |
| _version_ | 1797266614456942592 |
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| author | M. J. Vasli K. Babaei Velni M. R. Mohammadi Mozaffar A. Mollabashi M. Alishahiha |
| author_facet | M. J. Vasli K. Babaei Velni M. R. Mohammadi Mozaffar A. Mollabashi M. Alishahiha |
| author_sort | M. J. Vasli |
| collection | DOAJ |
| description | Abstract We investigate various aspects of the Lanczos coefficients in a family of free Lifshitz scalar theories, characterized by their integer dynamical exponent, at finite temperature. In this non-relativistic setup, we examine the effects of mass, finite ultraviolet cutoff, and finite lattice spacing on the behavior of the Lanczos coefficients. We also investigate the effect of the dynamical exponent on the asymptotic behavior of the Lanczos coefficients, which show a universal scaling behavior. We carefully examine how these results can affect different measures in Krylov space, including Krylov complexity and entropy. Remarkably, we find that our results are similar to those previously observed in the literature for relativistic theories. |
| first_indexed | 2024-04-25T01:03:29Z |
| format | Article |
| id | doaj.art-1e0ac93489dc4cd08ac694a27ce23a1c |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-04-25T01:03:29Z |
| publishDate | 2024-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-1e0ac93489dc4cd08ac694a27ce23a1c2024-03-10T12:20:32ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522024-03-0184311510.1140/epjc/s10052-024-12609-9Krylov complexity in Lifshitz-type scalar field theoriesM. J. Vasli0K. Babaei Velni1M. R. Mohammadi Mozaffar2A. Mollabashi3M. Alishahiha4Department of Physics, University of GuilanDepartment of Physics, University of GuilanDepartment of Physics, University of GuilanCenter for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa OiwakechoSchool of Physics, Institute for Research in Fundamental Sciences (IPM)Abstract We investigate various aspects of the Lanczos coefficients in a family of free Lifshitz scalar theories, characterized by their integer dynamical exponent, at finite temperature. In this non-relativistic setup, we examine the effects of mass, finite ultraviolet cutoff, and finite lattice spacing on the behavior of the Lanczos coefficients. We also investigate the effect of the dynamical exponent on the asymptotic behavior of the Lanczos coefficients, which show a universal scaling behavior. We carefully examine how these results can affect different measures in Krylov space, including Krylov complexity and entropy. Remarkably, we find that our results are similar to those previously observed in the literature for relativistic theories.https://doi.org/10.1140/epjc/s10052-024-12609-9 |
| spellingShingle | M. J. Vasli K. Babaei Velni M. R. Mohammadi Mozaffar A. Mollabashi M. Alishahiha Krylov complexity in Lifshitz-type scalar field theories European Physical Journal C: Particles and Fields |
| title | Krylov complexity in Lifshitz-type scalar field theories |
| title_full | Krylov complexity in Lifshitz-type scalar field theories |
| title_fullStr | Krylov complexity in Lifshitz-type scalar field theories |
| title_full_unstemmed | Krylov complexity in Lifshitz-type scalar field theories |
| title_short | Krylov complexity in Lifshitz-type scalar field theories |
| title_sort | krylov complexity in lifshitz type scalar field theories |
| url | https://doi.org/10.1140/epjc/s10052-024-12609-9 |
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