标题： 精确可解模型与普适算符生长 显示英文标题

标题： Exactly solvable models for universal operator growth

摘要： 量子可观测量在算符的克利诺夫（Krylov）空间中表现出一种普遍的增长模式。 这种模式在兰措斯（Lanczos）基底中尤为明显，在该基底下，演化超算符呈现三对角形式。 根据普适算符增长假设，超算符的非零元素——即兰措斯系数——渐近线性增长。 我们引入并研究了广泛的一类兰措斯系数，这些系数与普适算符增长一致，并导致精确可解的动力学。 在这些系数族内，兰措斯序列的渐近展开式的次主导项可以被控制和微调，以产生多样的动力学模式。 对于其中一个系数族，克利诺夫复杂度被精确计算。 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.