标题： 精确可解模型用于通用算子增长 显示英文标题

标题： Exactly solvable models for universal operator growth

摘要： 通用多体系统的量子可观测量在算符的Krylov空间中表现出增长的普遍模式。 这种模式在Lanczos基中尤为明显，其中演化超算符呈现出三对角形式。 根据普遍算符增长假说，超算符的非零元素，即Lanczos系数，渐近线性增长。 我们引入并探索了与普遍算符增长一致的Lanczos系数的广泛族，并导致精确可解的动力学。 在这些族中，Lanczos序列渐近展开的次主导项可以被控制和微调，以产生多种动力学模式。 对于其中一个族，Krylov复杂度被精确计算。 显示英文摘要

摘要： Quantum observables of generic many-body systems exhibit a universal pattern of growth in the Krylov space of operators. This pattern becomes particularly manifest in the Lanczos basis, where the evolution superoperator assumes the tridiagonal form. According to the universal operator growth hypothesis, the nonzero elements of the superoperator, known as Lanczos coefficients, grow asymptotically linearly. We introduce and explore broad families of Lanczos coefficients that are consistent with the universal operator growth and lead to the exactly solvable dynamics. Within these families, the subleading terms of asymptotic expansion of the Lanczos sequence can be controlled and fine-tuned to produce diverse dynamical patterns. For one of the families, the Krylov complexity is computed exactly.