Higher-Order Krylov State Complexity in Random Matrix Quenches

• URL: http://arxiv.org/abs/2412.16472v1
• Date: Sat, 21 Dec 2024 03:59:30 GMT
• Title: Higher-Order Krylov State Complexity in Random Matrix Quenches
• Authors: Hugo A. Camargo, Yichao Fu, Viktor Jahnke, Keun-Young Kim, Kuntal Pal,
• Abstract summary: In quantum many-body systems, time-evolved states typically remain confined to a smaller region of the Hilbert space known as the $textitKrylov subspace$. We investigate the time evolution of generalized spread complexities following a quantum quench in random matrix theory.
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• Abstract: 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.

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