Quantum many-body operator cascade as a route to chaos

Abstract:We describe a chaos scenario valid for chaotic many-body quantum systems, the simulation of which is one of the prime candidates for demonstrating quantum advantage, and clarify its importance for classical truncation-based simulations. By studying the spectral properties of the truncated propagator, we, for the first time, identify fractal structures responsible for many-body quantum chaos, analogous to the fractality in classical chaos emerging from the time evolution of initially smooth long-wavelength densities into ever finer short-wavelength densities. Namely, we show that the leading slowest-decaying Ruelle-Pollicott eigenoperators have a non-trivial fractal dimension quantifying their non-locality, visible also in the divergence of their condition numbers. Furthermore, we find that unitarity imposes an asymptotic equality between the temporal decay rate of local correlations and this many-body fractal dimension. With this insight, the scenario for many-body quantum chaos becomes clear: over time, local operators evolve toward increasingly non-local ones with a quantifiable fractal structure, thereby naturally leading to effective non-unitary relaxation on the subspace of local operators -- a kind of many-body Kolmogorov cascade in the space of operators -- which enables accurate truncation-based simulations. Our predictions are demonstrated numerically in various one- and two-dimensional quantum circuits, with and without conservation laws, as well as by exact results in dual-unitary circuits.

18 + 9 pages. Extended results also to systems with conservation laws and 2D systems, more detailed results on many-body fractality, better presentation

Statistical Mechanics (cond-mat.stat-mech); Chaotic Dynamics (nlin.CD); Quantum Physics (quant-ph)

arXiv:2604.16720 [cond-mat.stat-mech]

(or arXiv:2604.16720v2 [cond-mat.stat-mech] for this version)