Higher-order Krylov state complexity in random matrix quenches
Abstract In quantum many-body systems, time-evolved states typically remain confined to a smaller region of the Hilbert space known as the Krylov subspace. The time evolution can be mapped onto a one-dimensional problem of a particle moving on a chain, where the average position 〈n〉 defines Krylov s...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-07-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP07(2025)182 |
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| author | Hugo A. Camargo Yichao Fu Viktor Jahnke Keun-Young Kim Kuntal Pal |
| author_facet | Hugo A. Camargo Yichao Fu Viktor Jahnke Keun-Young Kim Kuntal Pal |
| author_sort | Hugo A. Camargo |
| collection | DOAJ |
| description | Abstract In quantum many-body systems, time-evolved states typically remain confined to a smaller region of the Hilbert space known as the Krylov subspace. The time evolution can be mapped onto a one-dimensional problem of a particle moving on a chain, where the average position 〈n〉 defines Krylov state complexity or spread complexity. Generalized spread complexities, associated with higher-order moments 〈n p 〉 for p > 1, provide finer insights into the dynamics. We investigate the time evolution of generalized spread complexities following a quantum quench in random matrix theory. The quench is implemented by transitioning from an initial random Hamiltonian to a post-quench Hamiltonian obtained by dividing it into four blocks and flipping the sign of the off-diagonal blocks. This setup captures universal features of chaotic quantum quenches. When the initial state is the thermofield double state of the post-quench Hamiltonian, a peak in spread complexity preceding equilibration signals level repulsion, a hallmark of quantum chaos. We examine the robustness of this peak for other initial states, such as the ground state or the thermofield double state of the pre-quench Hamiltonian. To quantify this behavior, we introduce a measure based on the peak height relative to the late-time saturation value. In the continuous limit, higher-order complexities show increased sensitivity to the peak, supported by numerical simulations for finite-size random matrices. |
| format | Article |
| id | doaj-art-f5da869d4eab47e18b09d6a68800a5bb |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-f5da869d4eab47e18b09d6a68800a5bb2025-08-20T04:01:42ZengSpringerOpenJournal of High Energy Physics1029-84792025-07-012025713410.1007/JHEP07(2025)182Higher-order Krylov state complexity in random matrix quenchesHugo A. Camargo0Yichao Fu1Viktor Jahnke2Keun-Young Kim3Kuntal Pal4Department of Physics and Photon Science, Gwangju Institute of Science and TechnologyDepartment of Physics and Photon Science, Gwangju Institute of Science and TechnologyDepartment of Physics and Photon Science, Gwangju Institute of Science and TechnologyDepartment of Physics and Photon Science, Gwangju Institute of Science and TechnologyDepartment of Physics and Photon Science, Gwangju Institute of Science and TechnologyAbstract In quantum many-body systems, time-evolved states typically remain confined to a smaller region of the Hilbert space known as the Krylov subspace. The time evolution can be mapped onto a one-dimensional problem of a particle moving on a chain, where the average position 〈n〉 defines Krylov state complexity or spread complexity. Generalized spread complexities, associated with higher-order moments 〈n p 〉 for p > 1, provide finer insights into the dynamics. We investigate the time evolution of generalized spread complexities following a quantum quench in random matrix theory. The quench is implemented by transitioning from an initial random Hamiltonian to a post-quench Hamiltonian obtained by dividing it into four blocks and flipping the sign of the off-diagonal blocks. This setup captures universal features of chaotic quantum quenches. When the initial state is the thermofield double state of the post-quench Hamiltonian, a peak in spread complexity preceding equilibration signals level repulsion, a hallmark of quantum chaos. We examine the robustness of this peak for other initial states, such as the ground state or the thermofield double state of the pre-quench Hamiltonian. To quantify this behavior, we introduce a measure based on the peak height relative to the late-time saturation value. In the continuous limit, higher-order complexities show increased sensitivity to the peak, supported by numerical simulations for finite-size random matrices.https://doi.org/10.1007/JHEP07(2025)182Gauge-Gravity CorrespondenceHolography and Condensed Matter Physics (AdS/CMT) |
| spellingShingle | Hugo A. Camargo Yichao Fu Viktor Jahnke Keun-Young Kim Kuntal Pal Higher-order Krylov state complexity in random matrix quenches Journal of High Energy Physics Gauge-Gravity Correspondence Holography and Condensed Matter Physics (AdS/CMT) |
| title | Higher-order Krylov state complexity in random matrix quenches |
| title_full | Higher-order Krylov state complexity in random matrix quenches |
| title_fullStr | Higher-order Krylov state complexity in random matrix quenches |
| title_full_unstemmed | Higher-order Krylov state complexity in random matrix quenches |
| title_short | Higher-order Krylov state complexity in random matrix quenches |
| title_sort | higher order krylov state complexity in random matrix quenches |
| topic | Gauge-Gravity Correspondence Holography and Condensed Matter Physics (AdS/CMT) |
| url | https://doi.org/10.1007/JHEP07(2025)182 |
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