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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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-07-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP07(2025)182 |
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| Summary: | 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. |
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| ISSN: | 1029-8479 |