Higher-Order Krylov State Complexity in Random Matrix Quenches
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arXiv
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| Format: | Preprint |
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2024
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| author | Camargo, Hugo A. Fu, Yichao Jahnke, Viktor Kim, Keun-Young Pal, Kuntal |
| author_facet | Camargo, Hugo A. Fu, Yichao Jahnke, Viktor Kim, Keun-Young Pal, Kuntal |
| contents | In quantum many-body systems, time-evolved states typically remain confined to a smaller region of the Hilbert space known as the $\textit{Krylov subspace}$. The time evolution can be mapped onto a one-dimensional problem of a particle moving on a chain, where the average position $\langle n \rangle$ defines Krylov state complexity or spread complexity. Generalized spread complexities, associated with higher-order moments $\langle n^p \rangle$ 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16472 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher-Order Krylov State Complexity in Random Matrix Quenches Camargo, Hugo A. Fu, Yichao Jahnke, Viktor Kim, Keun-Young Pal, Kuntal High Energy Physics - Theory Quantum Physics In quantum many-body systems, time-evolved states typically remain confined to a smaller region of the Hilbert space known as the $\textit{Krylov subspace}$. The time evolution can be mapped onto a one-dimensional problem of a particle moving on a chain, where the average position $\langle n \rangle$ defines Krylov state complexity or spread complexity. Generalized spread complexities, associated with higher-order moments $\langle n^p \rangle$ 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. |
| title | Higher-Order Krylov State Complexity in Random Matrix Quenches |
| topic | High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2412.16472 |