Новые и хорошо забытые старые подходы к квантовой многочастичной динамике: универсальность роста операторов, резонансы Руэля-Поликотта и разложение по псевдомодам

In the Heisenberg representation, a quantum observable evolves in a space of operators. In the many-body case this space is exponentially large, and the evolution is, at first sight, exponentially complex. On closer examination, however, it turns out that major simplifications can occur. The first one is the universal pattern of operator evolution discovered recently in [1]. The second one is the emergence of quantum many-body Ruelle-Pollicott resonances [2] that determine the large-time behavior of observables and correlation functions. Molding these two insights with the power of parallel computing, we are able to efficiently address quantum many-body dynamics directly in the thermodynamic limit and in systems inaccessible by other methods [3,4]. I will report on these advances.
[1] D. E. Parker, X. Cao, A. Avdoshkin, T. Scaffidi and E. Altman, A universal operator growth hypothesis, Phys. Rev. X, 9, 041017 (2019). [2] T. Prosen, Ruelle resonances in quantum many-body dynamics, J. Phys. A: Math. Gen. 35, L737 (2002). [3] F. Uskov, O. Lychkovskiy. Quantum dynamics in one and two dimensions via the recursion method, Phys. Rev. B 109, L140301 (2024). [4] A. Teretenkov, F. Uskov and O. Lychkovskiy, Pseudomode expansion of many-body correlation functions, arXiv 2407.12495